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All Textbook Solutions for Statistics for The Behavioral Sciences (MindTap Course List)

A researcher interested in the texting habits of high school students in the United States. The researcher selects a group, of 100 students, measures the number of text message that each individual sends each day, and calculate. the average number for the group. Identify the population for this study. Identify the sample for this study. The average number that the researcher calculated is, an example of a ________.2. Define the terms population, sample, parameter and statistic.WW3. Statistical methods are classified into two categories: descriptive and inferential. Describe the general purpose for the statistical methods in each category.Define the concept of sampling error and explain why this phenomenon creates a problem to be addressed by inferential statistics.Describe the data for a correlational research study. Explain how these data are different from the data obtained in experimental and nonexperimental studies, which also evaluate relationships between two variables.Describe how the goal of an experimental research study is different from the goal for nonexperimental or correlational research. Identify the two elements that are necessary for an experiment to achieve its goal.Stephens, Atkins, and Kingston (2009) conducted an experiment in which participants were able to tolerate more pain when they were shouting their favorite swear words than when they were shouting neutral words. Identify the independent and dependent variables for this study.8. 2 and age 4 compared to children who drank whole or 2% milk (Scharf, Demmer, and DeBoer, 2013). Is this an example of an experimental or a nonexperimental study?Gentile, Lynch, Linder, and Walsh (2004) surveyed over 600 8th- and 9th-grade students asking about their gaming habits and other behaviors. Their results showed that the adolescents who experienced more video game violence were also more hostile and had more frequent arguments with teachers. Is this an experimental or a nonexperimental study? Explain your answer.10. Weinstein, McDermott, and Roediger (2010) conducted an experiment to evaluate the effectiveness of different study strategies. One part of the study asked students to prepare for a test by reading a passage. In one condition, students generated and answered questions after reading the passage. In a second condition, students simply read the passage a second time. All students were then given a test on the passage material and the researchers recorded the number of correct answers. a. Identify the dependent variable for this study. b. Is the dependent variable discrete or continuous? c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?A research study reports that alcohol consumption is significantly higher for students at a state university than for students at a religious college (Wells, 2010). Is this study an example of an experiment? Explain why or why not.12. In an experiment examining the effects Tai Chi on arthritis pain, Callahan (2010) selected a large sample of individuals with doctor-diagnosed arthritis. Half of the participants immediately began a Tai Chi course and the other half (the control group) waited 8 weeks before beginning. At the end of 8 weeks, the individuals who had experienced Tai Chi had less arthritis pain that those who had not participated in the course. a. Identify the independent variable for this study. b. What scale of measurement is used for the independent variable? C. Identify the dependent variable for this study. d. What scale of measurement is used for the dependent variable?A tax form asks people to identify their annual income, number of dependents, and social security number. For each of these three variables, identify the scale of measurement that probably is used and identify whether the variable is continuous or discrete.Four scales of measurement were introduced in this chapter: nominal, ordinal, interval, and ratio. a. What additional information is obtained from measurements on an ordinal scale compared to measurements on a nominal scale? b. What additional information is obtained from measurements on an interval scale compared to measurements on an ordinal scale? c. What additional information is obtained from measurements on a ratio scale compared to measurements on an interval scale?Knight and Haslam (2010) found that office workers who had some input into the design of their office space were more productive and had higher well-being compared to workers for whom the office design was completely controlled by an office manager. For this study, identify the independent variable and the dependent variable.16. Explain why honesty is a hypothetical construct instead of a concrete variable. Describe how shyness might be measured and defined using an operational definition.Ford and Torok (2008) found that motivational signs were effective in increasing physical activity on a college campus. Signs such as 'Step up to a healthier lifestyle" and "An average person burns 10 calories a minute walking up the stairs" were posted by the elevators and stairs in a college building. Students and faculty increased their use of the stairs during times that the signs were posted compared to times when there were no signs. a. Identify the independent and dependent variables for this study. b. What scale of measurement is used for the independent variable?18 . 18. For the following scores, find the value of each expression: X 3 5 0 2 X X2 X+1 (X+1)19. For the following scores, find the value of each expression: X 3 2 5 1 3 X2 (X)2 (X1) (X1)2 20. For the following scores, find the value of each expression: X 6 2 0 1 3 1 X X2 (X+3)Two scores, X and Y, are recorded for each of n = 4 subjects. For these scores, find the value of each expression. X Y XY Subject X Y A 3 4 B 0 7 C 1 5 D 2 2 22. Use summation notation to express each of the following calculations: a. Add the scores and then add then square the sum. b. Square each score and then add the squared values. c. Subtract 2 points from each score and then add the resulting values. d. Subtract 1 point from each score and square the resulting values. Then add the squared values.23. For the following set of scores, find the value of each expression: X 1 6 2 3 X2 (X)2 (X3) (X3)2 Place the following set of n = 20 scores in a frequency distribution table. 6, 2, 2, 1, 3, 2, 4, 7, 1, 2 5, 3, 1, 6, 2, 6, 3, 3, 7, 2 Construct a frequency distribution table for the following set of scores. Include columns for proportion and percentage in your table. Scores: 2, 7, 5, 3, 2, 9, 6, 1, 1, 2 3, 3, 2, 4, 5, 2, 5, 4, 6, 5 Find each value requested for the distribution of scores in the following table. X Y 5 1 4 3 3 4 2 5 1 2 n X X2 Find each value requested for the distribution of scores in the following table. X Y 6 1 5 2 4 2 3 4 2 3 1 2 n X X2 For the following scores, the smallest value is X = 13 and the largest value is X = 52. Place the scores in a grouped frequency distribution table, a. Using an interval width of 5 points. b. Using an interval width of 10 points. , 25, 43, 19, 30, 27, 23, 18, , 17, 24, 16, 25, 49, 52, 47, , 18, 32, 24, 36, 26, 13, 25 The following scores are the ages for a random sample of n = 30 drivers who were issued speeding tickets in New York during 2008. Determine the best interval width and place the scores in a grouped frequency distribution table. From looking at your table, does it appear that tickets are issued equally across age groups? , 24, 22, 32, 30, 21, 44, 25, 45, 34, 36, 28, 20, 38, , 22, 39, 22, 56, 51, 53, 29, 20, 26, 28, 64, 23, , 19, 58,For each of the following samples, determine the interval width that is most appropriate for a grouped frequency distribution and identify the approximate number of intervals needed to cover the range of scores. a. Sample scores range from X = 8 to X = 41 b. Sample scores range from X = 16 to X = 33 c. Sample scores range from X = 26 to X = 98 What information is available about the scores in a regular frequency distribution table that you cannot obtain for the scores in a grouped table?Describe the difference in appearance between a bar graph and a histogram and describe the circumstances in which each type of graph is used.For the following set of scores: 5, 9, 6, 8, 7, 4, 10, 6, 7 7, 9, 9, 5, 8, 8, 6, 7, 10 a. Construct a frequency distribution table to organize the scores. b. Draw a frequency distribution histogram for these A survey given to a sample of college students contained questions about the following variables. For each variable, identify the kind of graph that should be used to display the distribution of scores (histogram, polygon, or bar graph). a. Number of brothers and sisters b. Birth-order position among siblings (oldest = 1") c. Gender (male/female) d. Favorite television show during the previous year Gaucher, Friesen, and Kay (2010) found that masculine-themed words (such as competitive, independent, analyze, strong) are commonly used in job recruitment materials, especially for job advertisements in male-dominated areas. In a similar study, a researcher counted the number of masculine-themed words in job advertisements for job areas, and obtained the following data. Area Number of Masculine Words Plumber 14 Electrician 12 Security guard 17 Bookkeeper 9 Nurse 6 Early-childhood educator 7 Determine what kind of graph would be appropriate for showing this distribution and sketch the frequency distribution graph.Find each of the following values for the distribution shown in the following polygon. n SW X X2 Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of the distribution? 13, 14, 12, 15, 15, 14, 15, 11, 13, 14 11, 13, 15, 12, 14, 14, 10, 14 ,13, 15 For the following set of scores: 9, 6, 7, 5, 4, 10, 8, 9, 5, 7, 2, , 7, 8, 8, 7, 4, 6, 3, 8, 9, 9, 6 Construct a frequency distribution table. Sketch a histogram showing the distribution. Describe the distribution using the following characteristics: (1) What is the shape of the distribution? (2) What score best identifies the center (average) for the distribution? (3) Are the scores clustered together, or are they spread out across the scale?Recent research suggests that the amount of time that parents spend talking about numbers can have a big impact on the mathematical development of their children (Levine, Suriyakham, Rowe, Huttenlocher, & Gunderson, 2010). In the study, the researchers visited the children's homes between the ages of 14 and 30 months and recorded the amount of "number talk" they heard from the children's parents. The researchers then tested the children's knowledge of the meaning of numbers at 46 months. The following data are similar to the results obtained in the study. Children's Knowledge-of-Numbers Scores for Two Groups of Parents Low Number-Talk Parents High Number-Talk Parents 2, 1, 2, 3, 4 3, 4, 5, 4, 5 3, 3, 2, 2, 1 4, 2, 3, 5, 4 5, 3, 4, 1, 2 5, 3, 4, 5, 4 Sketch a polygon showing the frequency distribution for children with low number-talk parents. In the same graph, sketch a polygon showing the scores for the children with high number-talk parents. (Use two different colors or use a solid line for one polygon and a dashed line for the other.) Does it appear that there is a difference between the two groups?Complete the final! two columns in the following frequency distribution table and then find the percentiles and percentile ranks requested: X f cf c% 5 2 4 5 3 6, 2 4 1 3 What is the percentile rank for X = 2.5? What is the percentile rank for X = 4.5? What is the 15th percentile? What is the 65th percentile?Complete the final two columns in the following frequency distribution table and then find the percentile. and percentile ranks requested: X f cf % 25-29 1 20-24 4 15-19 8 10-14 7 5-9 3 0-4 2 What is the percentile rank for X = 9.5? What is the percentile rank for X = 19.5? What is the 48th percentile? What is the '96th percentile?The following table shows four rows from a frequency distribution table for a sample of n = 25 scores. Use interpolation to find the percentiles and percentile ranks requested: X f cf c% 8 3 18 72 7 6 15 60 6 5 9 36 5 2 4 16 What is the percentile rank for X = 6? What is the percentile rank for X = 7? What is the 20th percentile? What is the 66th percentile?The following table shows four rows from frequency distribution table for a sample of n = 50 scores.. Use interpolation to find the percentiles and percentile ranks requested: X f cf c% 15 5 32 64 14 8 27 54 13 6 19 38 l2 4 13 26 What is the percentile rank for X = 13? What is the percentile rank for X = 15? What is the 50th percentile? What is the 60th percentile?The following table shows four rows. from a frequency dis1tribution table for a sample of n = 50 scores. Use interpolation to find the percentiles and percentile ranks requested: X f cf c% 15-19 3 50 100 10-14 6 47 94 5-9 8 41 82 0-4 18 33 66 What is the percentile rank for X = 17? What is the percentile rank for X = 6? What is the 70th percentile? d. What is the 90th percentile?22. The following table shows four rows. from a frequency dis1tribution table for a sample of n = 20 scores. Use interpolation to find the percentiles and percentile ranks requested: X f Cf C¾ 40-49 4 20 100 30-39 7 l6 80 20-29 4 9 45 10- 19 3 5 25 a. Find the 30th percentile. b. Find the 52nd percentile. c. What is the percentile rank for X = 46? d. What is the percentile rank for X = 21?Construct a stem and leaf display for the data in problem 5 using one stem for the scores in the 50s, one for scores in the 40s, and so on.A set of scores has been organized into the following stem and leaf display. For this set of scores: a. How many scores are in the 70s? b. Identify the individual scores in the 70s. c. How many scores are in the 40s? d. Identify the individual scores in the 40s.Use a stem and leaf display to organize the following distribution of scores. Use six stems with each stem corresponding to a 10-point interval. Scores: 36, 47, 14, 19, 65 52, 47, 42, 11, 25 28, 39, 32, 34, 58 57, 22, 49, 22, 16 33, 37, 23, 55, 44 Find the mean, median, and mode for the following sample of scores: 4, 5, 2, 7, 1, 3, 5 Find the mean, median, and mode for the following sample of scores: 6, 7, 3, 9, 8, 3, 7, 5 Find the mean, median, and mode for the scores in the following frequency distribution table: X F 6 5 2 4 2 3 2 2 2 1 5 Find the mean, median, and mode for the scores in the following frequency distribution table: Xf emsp;1 emsp; 1 emsp;2 55 42 emsp;2____ 32 For the following sample of n = 10 scores: a. Assume that the scores are measurements of a discrete variable and find the median. b. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. Scores: 2, 3, 4, 4, 5,A population of N = 15 scores has SX = 120. What is the population mean?A sample of n = 8 scores has a mean of M = 12. What is the value of EX for this sample?A population with a mean of = 8 has SX = 40. How many scores are in the population?One sample of n = 12 scores has a mean of M = 7 and a second sample of n = 8 scores has a mean of M = 12. If the two samples are combined, what is the mean for the combined sample?One sample has a mean of M = 8 and a second sample has a mean of M = 16. The two samples are combined into a single set of scores. a. What is the mean for the combined set if both of the original samples have n = 4 scores? b. What is the mean for the combined set if the first sample has n = 3 and the second sample has n = 5? c. What is the mean for the combined set if the first sample has n = 5 and the second sample has n = 3?One sample has a mean of M = 5 and a second sample has a mean of M = 10. The two samples are combined into a single set of scores. a. What is the mean for the combined set if both of the original samples have n = 5 scores? b. What is the mean for the combined set if the first sample has n = 4 scores and the second sample has n = 6? c. What is the mean for the combined set if the first sample has n = 6 scores and the second sample has n = 4?A population of N = 15 scores has a mean of = 8. One score in the population is changed from X = 20 to X = 5. What is the value for the new population mean?A sample of n = 7 scores has a mean of M = 16. One score in the sample is changed from X = 6 to X = 20. What is the value for the new sample mean?A sample of n = 9 scores has a mean of M = 20. One of the scores is changed and the new mean is found to be M = 22. If the changed score was originally X = 7, what is its new value?A sample of n = 7 scores has a mean of M = 9. If one new person with a score of X = I is added to the sample, what is the value for the new mean?A sample of n = 6 scores has a mean of M = 13. If one person with a score of X = 3 is removed from the sample, what is the value for the new mean?A sample of n = 15 scores has a mean of M = 6. One person with a score of X = 22 is added to the sample. What is the value for the new sample mean?A sample of n = 10 scores has a mean of M = 9. One person with a score of X = O is removed from the sample. What is the value for the new sample mean?A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new mean is found to be M = 6. What is the value of the new score? (Hint: Compare the values for EX before and after the score was added.)A population of N = 8 scores has a mean of = 16. After one score is removed from the population, the new mean is found to be = 15. What is the value of the score that was removed? (Hint: Compare the values for EX before and after the score was removed.)A sample of n = 9 scores has a mean of M = 13. After one score is added to the sample the mean is found to be M = 12. What is the value of the score that was added?Explain why the median is often preferred to the mean as a measure of central tendency for a skewed distribution.A researcher conducts a study comparing two different treatments with a sample of n = 16 participants in each treatment. The study produced the following data: Treatment 1: 6, 7, 11, 4, 19, 17, 2, 5, 9, 13, 6, 23, Treatment2: 10, 1, 11, 11, 1, 12, 7, 10,9 a. Calculate the mean for each treatment. Based on the two means, which treatment produces the higher scores? b. Calculate the median for each treatment. Based on the two medians, which treatment produces the higher scores? c. Calculate the mode for each treatment. Based on the two modes, which treatment produces the higher scores?Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were shown a list of sentences, of which half were humorous and half were non humorous. A humorous example is, "If at first you don't succeed, you are probably not related to the boss." Other participants would see a nonhumorous version of this sentence, such as "People who are related to the boss often succeed the very first time." Schmidt then measured the number of each type of sentence recalled by each participant. The following scores are similar to the results obtained in the study. Number of Sentence Recalled Humorous Nonhumorous Sentences Sentences 4 5 2 4 5 2 4 2 6 7 6 6 2 3 l 6 2 5 4 3 3 2 3 3 1 3 :5 5 4 1 5 3 Calculate the mean number of sentences recalled for each of the two conditions. Do the data suggest that humor help memory'?Stephens, Atkins, and Kingston (2009) conducted a research study demonstrating that swearing can help reduce pain. In the study, each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In one condition, the participants repeatedly yelled their favorite curse words while their hands were in the water. In the other condition the participants yelled a neutral word. Data similar to the results obtained in the study are shown in the following table. Calculate the mean number of seconds that the participants could tolerate the pain for each of the two treatment conditions. Does it appear that swearing helped with pain tolerance? Amount of Time (in seconds} l 94 59 2 70 61 3 52 47 4 83 60 5 46 35 6 117 92 7 69 53 8 39 30 9 51 56 10 73 6]In words, explain what is measured by SS, variance, and standard deviation.Is it possible to obtain a negative value for the variance or the standard deviation?Describe the scores in a sample that has standard deviation of zero.There are two different formulas or methods that can be used to calculate SS. Under what circumstance is the definitional formula easy to use? Under what circumstances is the computational formula preferred?Calculate the mean and S,S (sum of squared deviations) for each of the following samples. Based on the value for the mean you should be able to decide which SS formula is better to use.. Sample A:1,3,4,0 Samp1e B:2,5,0,3 Calculate ss, variance and standard deviation for the following population of N = 5 scores: 2, 13, 4. 10 6. (Note: The definitional formula works well with these scores.)Calculate ss. variance and standMd deviation for the following population of N "" 7 oores: s:. 1 4 3 S 3, ( N.01e: The definitional formula woriks well with these oores.),For the foUow.ing population of N=6 score: l ,4,33,4 Sketch a histogram showing the population distribution. Locate the value of the population mean in your sketch, and nrn.ke an estimate of the standard deviation (as done in Example 4.,2).. Compute SS, variance, and standard deviation for the population. (How well does your estimate com pare with the actual value of s?)For the fol1owing set of scores: 1, 4, 3, 5, 7 a. If the scores are a population what are the variance and standard deviation? b. If the scores are a sample, what are the variance and standard deviation?10P For the fol1owing sample of n = 6 scores: 0, 11, 5 , 5, 5 a. Sketch a histogram showing the sample distribution. b. Locate the value of the sample mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.6). c. Compute SS variance, and standard deviation for the ample. (How well does your estimate compare with the actual value of s?)12. Calculate SS, variance and standard deviation for the following sample of n = 8 score: 0, 4, 1, 3, 2, 1, 1, 0.13P A population has a mean of µ = 50 and a standard deviation of s = 10. If 3 points were added to every score in the population, what would be the new values for the mean and standard deviation? If every sore in the population were multiplied by 2, then what would be the new value for the mean and standard deviation?a. After 6 points have been added to every score in a sample the mean is found to be M = 10 and the standard deviation is s = 13. What were the values for the mean and standard deviation for the original sample? b. After every score in a sample is multiplied by 3, the mean is found to be M = 48 and the standard deviation is .f = l 8 what were the values for the mean and standard deviation for the original sample?16. Compute the mean and standard deviation for the following sample of n = 4 scores: 82, 88, 82 and 86, Hint: To simplify the arithmetic you can subtracted 80 points from each score to obtain a new sample consisting of 2, 8, 2 and 6. Then, compute the mean and standard deviation for the new sample. Use the values you obtain to find the mean and standard deviation for the original sample For the following sample of n = 8 scores: 0, 1, ½, 0, 3, ½, 0, and 1: Simp1ify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 0 and 2. Then, compute the mean and standard deviation for the new sample. Using the value you obtained in part a, what are the values for the mean and standard deviation for the original sample?For the following population of N=6 scores 9,6,8,9,8 a. Calculate the range and the standard deviation. (Use either definition for the range) b. Add 2 points to each score and compute the range and standard deviation again. Describe how adding a constant to each score influence measures of variability.The range is completely determined by the two extreme scores in a distribution. The standard deviation on the, other hand uses every score. Compute the range (choose either definition) and the standard deviation for the following sample of n = 5 scores. Note that there are three score clustered around the mean in the center of the distribution and two extreme values. Scores:0,6,7,8,14. Now we will break up the cluster in the center of the distribution by moving two of the central scores out to the extremes. Once again compute the range and the standard deviation. New scores:0,0,7,14,14. According to the range how do the two distributions compare in variability? How do they compare according to the standard deviation?For the data in the following sample: ,6,8,6,5 Find the mean and the standard deviation. Now change the score of X = l0 to X = 0 and find the new mean and standard deviation. Describe how one extreme score influences the mean and standard deviation.21 . Within a population. the differences that exist from one person to another are often called diversity. Researchers comparing cognitive kills for younger adults and older adults typically find greater difference. (greater diversity ,in the older population (Morse, 1993). Following are typical data showing problem-solving scores for two groups of participants. Older Adults (average age 72) 738 845 266 Younger Adults (average age 31) 678 668 869 Compute the me.an, variance. and standard deviation for each group. Is one group of scores 111.oticeabty more variable (more diverse) than the other?Wegesin and Stern (2004) found greater consistency (less variability) in the memory performance scores for younger women than for older women. The following data represent memory scores obtained for two women, one older and one younger, over a series of memory trials. Younger Older 8 7 6 5 6 8 7 5 8 7 7 6 8 8 8 5 Calculate the variance of the scores for each woman. Are the scores for the younger woman more consistent (less variable)?A population has a mean of =50 and a standard deviation of =20 . Would a score of X=70 be considered an extreme value (out in the tail) in this sample? If the standard deviation were =5 , would a score of X=70 be considered an extreme value?On an exam with a mean of M=78 , you obtain a score of X=84 . Would you prefer a standard deviation of s=2 or s=10 ? (Hint: Sketch each distribution and find the location of your core.) If your score were X=72 , would you prefer s=2 or s=10 ? Explain your answer.What information is provided by the sign (+/)of a z-score? What information is provided by the numerical value of the z-score?A distribution has a standard deviation of =10. Find the z-score for each of the following locations in the distribution. Above the mean by 5 points. Above the mean by 2 points. Below the mean by 20 points. Below the mean by 15 points.For a distribution with a standard deviation of =20, describe the location of each of the following z-scores in terms of its position relative to the mean. For example, z=+1.0is a location that is 20 points above the mean. z=+2.00 z=+0.50 z=1.00 z=0.25 For a population with =60and =12 Find the a-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.) X=75X=48X=84X=54X=78X=51 Find the score (X value) that corresponds to each of the following z-scores. (Again, you should not need a formula or any serious calculations.) z=1.00z=0.25z=1.50z=0.50z=1.25z=2.50 For a population with =40and =11 , find the a-score for each of the following X values. (Note: You probably will need to use a formula and a calculator to find these values.) X=45X=52X=41X=30X=25X=38 For a population with a mean of =100and a standard deviation of =20 , Find the a-score for each of the following X values. X=108X=115X=130X=90X=88X=95 Find the score (X value) that corresponds to each of the following z-scores. z=0.40z=0.50z=1.80z=0.75z=1.50z=1.25 A population has a mean of =60and a standard deviation of =12. For this population, find the z-score for each of the following X values. X=69X=84X=63X=54X=48X=45 For the same population, find the score (X value) that corresponds to each of the following a-scores. z=0.50z=1.50z=2.50z=0.25z=0.50z=1.25 Find the a-score corresponding to a score of X=45 for each of the following distributions. =40and=20 =40and=10 =40and=5 =40and=2 Find the X value corresponding to z=0.25 of the following distributions. =40and=4 =40and=8 =40and=16 =40and=32 A score that is 6 points below the mean corresponds to a z-score of z=2.00. What is the population standard deviation?A score that is 9 points above the mean corresponds to a z-score of z=1.50. What is the population standard deviation?For a population with a standard deviation of ( =12, a score of X=44corresponds to z=0.50. What is the population mean?For a population with a mean of =70, a score of X=64corresponds to z=1.50. What is the population standard deviation?In a population distribution, a score of X=28corresponds to z=1.00 and a score of X=34corresponds to z=0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.)For each of the following populations, would a score of X=85 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)? =75and=15 =80and=2 =90and=20 =93and=3 A distribution of exam scores has a mean of =78. If your score is X=70, which standard deviation would give you a better grade: =4or =8? If your score is X=80, which standard deviation would give you a better grade: =4or =8?For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer. A score of X=70, on an exam with M=82and =8; or a score of X=60on an exam with =72and =12. A score of X=58, on an exam with =49and =6; or a score of X=85on an exam with =70and =10. A score of X=32, on an exam with =24and =4; or a score of X=26on an exam with =20and =2.A distribution with a mean of =38and a standard deviation of =5is transformed into a standardized distribution with =50and =10. Find the new, standardized score for each of the following values from the original population. X=39 X=43 X=35 X=28 A distribution with a mean of =76and a standard deviation of =12is transformed into a standardized distribution with =100and =20. Find the new, standardized score for each of the following values from the original population. X=61 X=70 X=85 X=94 A population consists of the following N=5scores: 0, 6, 4, 3, and 12. Compute and for the population. Find the z-score for each score in the population. Transform the original population into a new population of N=5scores with a mean of =100and a standard deviation of =20.A sample has a mean of M=30and a standard deviation of s=8. Find the z-score for each of the following X values from this sample. X=32X=34X=36X=28X=20X=18 A sample has a mean of M=25and a standard deviation of s=5. For this sample, find the X value corresponding to each of the following z-scores. z=0.40z=1.20z=2.00z=0.80z=0.60z=1.40 For a sample with a standard deviation of s=8, a score of X=65 corresponds to z=1.50. What is the sample mean?For a sample with a mean of M=51, a score of X=59corresponds to z=2.00. What is the sample standard deviation?In a sample distribution, X=56corresponds to z=1.00, and X=47corresponds to z=0.50. Find the mean and standard deviation for the sample.A sample consists of the following n=7 scores: 5, 0, 4, 5, 1, 2, and 4. a. Compute the mean and standard deviation for the sample. b. Find the z-score for each score in the sample. c. Transform the original sample into a new sample with a mean of M=50and s=10.What are the two requirements for a random sample?Define sampling with replacement and explain why is it used?Around Halloween each year the grocery store sells three -pound bags of candy contains a mixture of three different mini-bars: Snickers, Milky Way and Twix. If the bag has an equal number of each of the three bars then what are the probabilities for each of the following? Randomly selecting a Milky Way bar. Randomly selecting either a Snickers or Twix bar. Randomly selecting something other than a Twix Bar.A psychology class consists of 28 males and 52 females. If the professor selects names from the class list using random sampling, What is the probability that the first student selected will be a female? If a random sample of n=3students is selected and the first two are both females, what is the probability that the third student selected will be a male?5. Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the tail is on the right or left side of the line and find the proportion in the tail. a. z=1.00 b. z=0.50 c. z=1.25 d. z=0.40 Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body. a. z=2.50 b. z=0.80 c. z=0.50 d. z=0.77 Find each of the following probabilities for a normal distribution. a. p(z1.25) b. p(z0.60) c. p(z0.70) d. p(z1.30)S. What proportion of a normal distribution is located between each of the following z-score boundaries? a. z = -0.25 and z = +0.25 b. z = -0.67 and z= +0.67 c. z = -l.20 and z = +1.20 Find each of the following probabilities for a normal distribution. a. p (-0.80 < z< 0.80 ) b. p(-0.50 < z< 1.00) C . p (0.20 < z < 1.50) d. p(-1.20 < z< -0.80 )10. Find the z-score location of a vertical line that separates a normal distribution as described in each of the following. a. 5% in the tail ,on the left b. 30% in the tail on the right c. 65% in the body on the left d. 80% in the body on the right Find the z-score boundaries that separate a normal distribution as described in each of the following. The middle 30% from the 70% in the tails. The middle 40% from the 60% in the tails. The middle 50% from the 50% in the tails. d. The middle 60% from the 40% in the tails.A normal distribution has a mean of =70 and a Standard deviation of =8. For each of the following Scores indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the tail. X = 72 X = 76 c. X = 66 d.. X= 60 13. A normal distribution has a mean .of µ=30 and a standard deviation of =12.For each ,of the following core indicate whether the body is to the right or left of the core and find the proportion of the distribution located in the body. a. X= 33 b. X= l 8 c. x= 24 d. X= 39 For a normal distribution with a mean of =60and a standard deviation of =10 ,find the proportion of the population corresponding to ,each of the following . Scores greater than 65. Scores less than 68. Scores between 50 and 70.15. In 20l4, the New York Yankees had a team batting average of µ = 245 (actually 0.245 but we will avoid the decimals. Of course, the batting average varies from game to game but assuming that the distribution of batting averages for l62 games is normal with a standard deviation of a = 40 points, answer each of the following. lf you random]y select one game from 2014, what is the probability that the team batting average was over 300? If you randomly select one game from 2014, what is the probability that the team batting average was under 200?16. IQ test scores are standardized to produce a normal distribution with a mean of µ = 100 and a standard deviation of =15. Find the proportion of the population in each of the following IQ categories. Genius or near genius: IQ over 140 Very superior intelligence : IQ from 120-140 Average or normal intelligence : IQ from 90-109 The distribution of scores on the SAT is approximately normal with a mean of µ = 500 and a standard deviation of =100. For the population of students who have taken the SAT, What proportion have SAT score less than 400? What proportion have SAT score greater than 650? What is the minimum SAT score needed to be in the highest 20% of the population? , If the state college only accepts students from the top 40% of the SAT distribution, what is the minimum SAT score needed to be accepted?18. According to a recent report, people .smile an average .of =62times per day. Assuming that the distribution of smile is approximately normal with a standard deviation of =18. Find each of the following values. a. What proportion of people smile more than 80 times in a day? b. What proportion of people smile at least 50 times a day?A report in 20 l0 indicates that Americans between the ages of 8 and 18 spend an average of µ=7.5 hours per day using some sort of electronic device such as smart phones, computers, or tablets. Assume that: the distribution of times is normal with a standard deviation of =2.5hours and find the following values. What is the probability of electing an individual who uses electronic devices more than 12 hours a day? What proportion of 8 to 18 year- old Americans spend between 5 and l0 hours per day using electronic devices? In symbols, p(5 < X < 10) =?, Rochester, New York, averages µ = 2 l .9 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard deviation of =6.5inches. A local jewelry store advertised a refund of 50% off all purchase made in December, if we have more than 3 feet(36 inches) during the month. What is the probability that the jewelry store will have to pay off on its promise?A multiple-choice test has 32 questions, ,each with four response choices. If a student is simply guessing at the answers, What is the probability of guessing ,correctly for any individual question? On average, how many questions would a student answer correctly for the entire test? e., What is the probability that a student would. Get more than 12 answers correct simply by guessing?A true/false test has 20 questions. If a student is simply guessing at the answers, On average, how many questions would a student answer correctly for the entire test? What is the probability that a student would answer more than 15 questions correctly simply by guessing? What is the probability that a student would answer fewer than 7 questions correctly simply by f.guessing?A roulette wheel has alternating red and black numbered slots into which the ball finally stops to determine the winner. If a gambler always bets on black to win, then What is the probability of winning at least 40 times in a series of 64 spins? (Note that at lea.st 40 wins means 40 or more.) What is the probability of winning more than 40 times in a series of 64 spins? Based on your answers to a and b, what is the probability of winning exactly 40 times?A test developed to measure ESP involves using Zener cards. Each card shows one of five equally likely symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person who has no ESP and is just guessing. What is the probability of correctly predicting exactly 20 cards in a series of l00 trials? What is the probability of correctly predicting 10 or more cards in a series of 36 trials? What is the probability of correctly predicting more than 16 cards in a series sof 64 trials?The student health clinic reports that only 30%, of students got a flu shot this year. If a researcher surveys a sample of n = 84 students attending a basketball game, a. What is the probability that any individual student has had a flu shot? b, What is the probability that more than 30 students have had flu shots ? c. What is the probability that 20 or fewer students have had sshots?Briefly define each of the following: a. Distribution of sample means. b. Expected value of M. c. Standard error of M.A sample is selected from a population with a mean of =40 and a standard deviation of =8 . If the sample has n=4 scores, what is the expected value of M and the standard error of M? If the sample has n=16 scores, what is the expected value of M and the standard error of M?Describe the distribution of sample means (shape, mean, standard error) for samples of n=64 selected from a population with a mean of =90 and a standard deviation of =32 .The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not be normal?A population has a standard deviation of =24 . On average, how much difference should there be between the sample mean and the population mean for a random sample of n=4 scores from this population? On average, how much difference should there be for a sample of n=9 scores? On average, how much difference should there be for a sample of n=16 scores?For a population with a mean of =45 and a standard deviation of =10 , what is the standard error of the distribution of sample means for each of the following sample sizes? n=4 scores n=25 scores For a population with =12 , how large a sample is necessary to have a standard error that is: less than 4 points? less than 3 points? less than 2 points?If the population standard deviation is =10 , how large a sample is necessary to have a standard error that is less than 5 points? less than 2 points? less than 1 point?For a sample of n=16 scores, what is the value of the population standard deviation () necessary to produce each of the following a standard error values? M=8 points? M=4 points? M=1 point?For a population with a mean of =40 and a standard deviation of =8 , find the z-score corresponding to each of the following samples. X=36 for a sample of n=1 score M=36 for a sample of n=4 scores M=36 for a sample of n=16 scores A sample of n=25 scores has a mean of M=68 . Find the z-score for this sample: If it was obtained from a population with =10 and =60 . If it was obtained from a population with =20 and =60 . If it was obtained from a population with =40 and =60 .A population forms a normal distribution with a mean of =55 and a standard deviation of =12 . For each of the following samples, compute the z-score for the sample mean. M=58 for n=4 scores M=58 for n=16 scores M=58 for n=36 scores cores on a standardized reading test for 4th-grade students form a normal distribution with =60 and =20 . What is the probability of obtaining a sample mean greater than M=65 for each of the following: a sample of n=16 students a sample of n=25 students a sample of n=100 students IQ scores form a normal distribution with a mean of =100 and a standard deviation of =15 . What is the probability of obtaining a sample mean greater than M=103 for a random sample of n=9 people? for a random sample of n=25 people? for a random sample of n=100 people?A normal distribution has a mean of =54 and a standard deviation of =6 . What is the probability of randomly selecting a score less than x=51 ? What is the probability of selecting a sample of n=4 scores with a mean less than M=51 ? What is the probability of selecting a sample of n=36 scores with a mean less than M=51 ?A population has a mean of =30 and a standard deviation of =8 If the population distribution is normal, what is the probability of obtaining a sample mean greater than M=32 for a sample of n=4 If the population distribution is positively skewed, what is the probability of obtaining a sample mean greater than M=32 for a sample of n=4 If the population distribution is normal, what is the probability of obtaining a sample mean greater than M=32 for a sample of n=64 If the population distribution is positively skewed, what is the probability of obtaining a sample mean greater than M=32 for a sample of n=64 For random samples of size n=25 selected from a normal distribution with a mean of mean of =50 and a standard deviation of =20 , find each of the following: The range of sample means that defines the middle 95% of the distribution of sample means. The range of sample means that defines the middle 99% of the distribution of sample means.The distribution ages for students at the state college is positively skewed with a mean of =21.5 and a standard deviation of =3 . What is the probability of selecting a random sample of n=4 students with an average age greater than 23? (Careful: This is a trick question.) What is the probability of selecting a random sample of n=36 students with an average age greater than 23? For a sample of n=36 students, what is the probability that the average age is between 21 and 22?Jumbo shrimp are those that require 1015 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages =12.5 with a standard deviation of =1 , and forms a normal distribution. What is the probability of randomly picking a sample of n=25 1-pound bags that average more than M=13 shrimp per bag?Callahan (2009) conducted a study to evaluate the effectiveness of physical exercise programs for individuals with chronic arthritis. Participants with doctor-diagnosed arthritis either received a Tai Chi course immediately or were placed in a control group to begin the course 8 weeks later. At the end of the 8-week period, self-reports of pain were obtained for both groups. Data similar to the results obtained in the study are shown in the following table. Self-Reported Level of Pain Mean SE Tai Chi course 3.7 1.2 No Tai Chi course 7.6 1.7 Construct a bar graph that incorporates all of the information in the table. Looking at your graph, do you think that participation in the Tai Chi course reduces arthritis pain?A normal distribution has a mean of =60 and a standard deviation of =18 . For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size. M=67 for n=4 scores M=67 for n=36 scores A random sample is obtained from a normal population with a mean of =95 and a standard deviation of =40 . The sample mean is M=86 . Is this a representative sample mean or an extreme value for a sample of n=16 scores? Is this a representative sample mean or an extreme value for a sample of n=100 scores?A normal distribution has a mean of =65 and a standard deviation of =20 . For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of its size. M=74 for a sample of 4 scores M=74 for a sample of 25 scores Identify the four steps of a hypothesis test as presented in this chapter.Define the alpha level and the critical region for a hypothesis test.Define a Type I error and a Type Il error and explain the consequences of each.If the alpha level is changed from =.05 to =.01 What happens to the boundaries for the critical region? What happens to the probability of a Type I error?The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following: a. Increasing the difference between the sample mean and the original population mean. b. Increasing the population standard deviation. c. Increasing the number of scores in the sample.Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research (Persson, Bringlov, Nilsson, and Nyberg, 2004). In a typical study, a researcher obtains a sample of n=16 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general population, scores from the test form a normal distribution with a mean of =50 and a standard deviation of =12 . The sample of research participants had an average of M=54 . a. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variables being examined. b. Using the standard 4-step procedure, conduct a two-tailed hypothesis test with =.05 to evaluate the effect of the supplements.Babcock and Marks (2010) reviewed survey data from 2003-2005, and obtained an average of =14 hours per week spent studying by full-time students at 4-year colleges in the United States. To determine whether this average has changed in the past 10 years, researcher selected a sample of n=64 of today’s college students and obtained an average of M=12.5 hours. If the standard deviation for the distribution is =4.8 hours per week, does this sample indicate a significant change in the number of hours spent studying? Use a two-tailed test with =.05 .Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, =50 and a standard deviation of =15 . The sample of group- participation adolescents had an average of M=53.8 . a. Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with =.05 . b. Compute Cohen’s d to measure the size of the difference. c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.The psychology department is gradually changing its curriculum by increasing the number of online course offerings. To evaluate the effectiveness of this change, a random sample of n=36 students who registered for Introductory Psychology is placed in the online version of the course. At the end of the semester, all students take the same final exam. The average score for the sample is M=76 . For the general population of students taking the traditional lecture class, the final exam scores form a normal distribution with a mean of =71 . a. If the final exam scores for the population have a standard deviation of =12 , does the sample provide enough evidence to conclude that the new online course is significantly different from the traditional class? Use a two-tailed test with =.05. b. If the population standard deviation is =18 , is the sample sufficient to demonstrate a significant difference? Again, use a two-tailed test with =.05 . c. Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.A random sample is selected from a normal population with a mean of =30and a standard deviation of =8 . After a treatment is administered to the individuals in the sample, the sample mean is found to be M=33 . a. If the sample consists of n=16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with =.05. b. If the sample consists of n=64 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with =.05. c. Comparing your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.A random sample of n=25scores is selected from a normal population with a mean of =40 . After a treatment is administered to the individuals in the sample, the sample mean is found to be M=44 . a. If the population standard deviation is =5 , is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with =.05. b. If the population standard deviation is =15, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with =.05. c. Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.Brunt, Rhee, and Zhong (2008) surveyed 557 undergraduate college students to examine their weight status, health behaviours, and diet. Using body mass index (BMI), they classified the students into four categories: underweight, healthy weight, overweight, and obese. They also measured dietary variety by counting the number of different foods each student ate from several food groups. Note that the researchers are not measuring the amount of food eaten, but rather the number of different foods eaten (variety, not quantity). Nonetheless, it was somewhat surprising that the four the four weight groups all ate essentially the same number of fatty and/or sugary snacks. Suppose a researcher conducting a follow up study obtains a sample of n=25 students classified as healthy weight and a sample of n=36 students classified as overweight. Each student completes the food variety questionnaire, and the healthy-weight group produces a mean of M=4.01 for the fatty, sugary snack category compared to a mean of M=4.48 for the overweight group. The results from the Brunt, Rhee, and Zhong study showed an overall mean score of =4.22 for the sweets or fats food group. Assume that the distribution of scores is approximately normal with a standard deviation of =0.60 . a. Does the sample of n=36 indicate that number of fatty, sugary snacks eaten by overweight students is significantly different from the overall population mean? Use a two-tailed test with =.05 . b. Based on the sample of n=25 healthy-weight students, can you conclude that healthy-weight students eat significantly fewer fatty, sugary snacks than the overall population? Use a one-tailed test with =.05 .A random sample is selected from a normal population with a mean of =100 and a standard deviation of =20 . After a treatment is administered to the individuals in the sample, the sample mean is found to be M=96 . a. How large a sample is necessary for this sample mean to be statistically significant? Assume a two-tailed test with =.05. b. If the sample mean were M=98 , what sample size is needed to be significant for a two-tailed test with =.05 ?In a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that even moderate alcohol consumption significantly slowed response time to an emergency situation in a driving simulation. In a similar study, researchers measured reaction time 30 minutes after participants consumed one 6-ounce glass of wine. Again, they used a standardized driving simulation task for which the regular population averages =400 msec. The distribution of reaction times is approximately normal with =40 . Assume that the researcher obtained a sample mean of M=422 for the n=25 participants in the study. a. Are the data sufficient to conclude that the alcohol has a significant effect on reaction time? Use a two-tailed test with =.01 . b. Do the data provide evidence that the alcohol significantly increased (slowed) reaction time? Use a one-tailed test with =.01 . c. Compute Cohen’s d to estimate the size of the effect.The researchers cited in the previous problem (Liguori and Robinson. 2001) also examined the effect of caffeine on response time in the driving simulator. In a similar study, researchers measured reaction time 30 minutes after participants consumed one 6-ounce cup of coffee. Using the same driving simulation task, for which the distribution of reaction times is normal with =400 msec and =40 , they obtained a mean of M=392 for a sample of n=36 participants. a. Are the data sufficient to conclude that caffeine has a significant effect on reaction time? Use a two- tailed test with =.05 . b. Compute Cohen’s d to estimate the size of the effect. c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.Researchers at a National Weather Center in the north-eastern United States recorded the number of 900 days each year since records first started in 1875. The numbers form a normal shaped distribution with a mean of =9.6 and a standard deviation of =1.9 . To see if the data showed any evidence of global warming, they also computed the mean number of 900 days for the most recent n=4 years and obtained M=12.25 . Do the data indicate that the past four years have had significantly more 900 days than would be expected for a random sample from this population? Use a one-tailed test with =.05 .A high school teacher has designed a new course intended to help students prepare for the mathematics section of the SAT. A sample of n=20 students is recruited to for the course and, at the end of the year, each student takes the SAT. The average score for this sample is M=562. For the general population, scores on the SAT are standardized to form a normal distribution with =500 and =100 . a. Can the teacher conclude that students who take the course score significantly higher than the general population? Use a one-tailed test with =.01 . h. Compute Cohen’s d to estimate the size of the effect. c. Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size would appear in a research report.Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidants in foods such as blueberries can reduce and even reverse these age-related declines, at least in laboratory rats (Joseph et at.. 1999). Based on these results, one might theorize that the same antioxidants might also benefit elderly humans. Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n=16 adults who are older than 65, and gives each participant a daily dose of a blueberry supplement that is very high in antioxidants. After taking the supplement for 6 months, the participants are given a standardized cognitive skills test and produce a mean score of M=50.2 . For the general population of elderly adults, scores on the test average =45 and form a normal distribution with =9 . a. Can the researcher conclude that the supplement has a significant effect on cognitive skill? Use a two-tailed test with =.05 . b. Compute Cohen’s d for this study. c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of =40 and a standard deviation of =12 . The researcher expects a 6-point treatment effect and plans to use a two-tailed hypothesis test with =.05 . a. Compute the power of the test if the researcher uses a sample of n=9 individuals. (See Example 8.6.) b. Compute the power of the test if the researcher uses a sample of n=16 individuals.A researcher plans to conduct an experiment evaluating the effect of a treatment. A sample of n=9 participants is selected and each person receives the treatment before being tested on a standardized dexterity task. The treatment is expected to lower scores on the test by an average of 30 points. For the regular population, scores on the dexterity task form a normal distribution with =240 and =30 . a. If the researcher uses a two-tailed test with =.05 , what is the power of the hypothesis test? b. Again assuming a two-tailed test with =.05, what is the power of the hypothesis test if the sample size is increased to n=25?Research has shown that IQ scores have been increasing for years (Flynn, 1984. 1999). The phenomenon is called the Flynn effect and the data indicate that the increase appears to average about 7 points per decade. To examine this effect, a researcher obtains an IQ test with instructions for scoring from 10 years ago and plans to administers the test to a sample of n=25 of today’s high school students. Ten years ago, the scores on this IQ test produced a standardized distribution with a mean of =100 and a standard deviation =15 . If there actually has been a 7-point increase in the average IQ during the past 10 years, then find the power of the hypothesis test for each of the following. a. The researcher uses a two-tailed hypothesis test with =.05 to determine if the data indicate a significant change in IQ over the past 10 years. b. The researcher uses a one-tailed hypothesis test with =.05 to determine if the data indicate a significant increase in IQ over the past 10 years.Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant. a. The size of the z-score in a hypothesis test. b. The size of Cohen’s d . c. The power of a hypothesis test.W23. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant. a. Increasing the alpha level from .01 to .05. b. Changing from a one-tailed test to a two-tailed test.Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?A sample of n=16 scores has a mean of M=56and a standard deviation of s=12 . a. Explain what is measured by the sample standard deviation. b. Compute the estimated standard error for the sample mean and explain what is measured by the standard error.Find the estimated standard error for the sample mean for each of the following samples. a. n=9 with SS=1152 b. n=16 with SS=540 c. n=25 with SS=600 Explain why tdistributions tend to be flatter and more spread out than the normal distribution.Find the t values that form the boundaries of the critical region for a two-tailed test with =.05 for each of the following sample sizes: a. n=4 b. n=15 c. n=24 Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailed test with =.01 for each of the following sample sizes. a. n=10 b. n=20 c. n=30 The following sample of n=4 scores was obtained from a population with unknown parameters. Scores: 2, 2, 6, 2 a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.) b. Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)The following sample was obtained from a population with unknown parameters. Scores: 13, 7, 6, 12, 0, 4 a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.) b. Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)A random sample of n=12 individuals is selected from a population with =70 , and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M=74.5 with SS=297 . a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.) b. How much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test. this value is the denominator of the t statistic.) c. Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with =.05 .A random sample of n=25 individuals is selected from a population with =20 , and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M=22.2 with SS=384 . a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the r statistic.) b. If there is no treatment effect, how much difference is expected between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.) c. Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with =.05.To evaluate the effect of a treatment, a sample is obtained from a population with a mean of =30 , and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M=31.3 with a standard deviation of =3 . a. tithe sample consists of n=16 individuals. are the data sufficient to conclude that the treatment has a significant effect using a two-tailed Lest with =.05 ? b. If the sample consists of n=36 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with =.05 ? c. Comparing your answer for parts a and b, how does the size of the sample influence the outcome of a hypothesis test?To evaluate the effect of a treatment, a sample of n=8 is obtained from a population with a mean of =40 , and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M=35 . a. If the sample variance is s2=32 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with =.05? b. If the sample variance is s2=72 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with =.05 ? c. Comparing your answer for pans a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?The spotlight effect refers to overestimating the extent to which others notice your appearance or behaviour, especially when you commit a social faux pas. Effectively, you feel as if you are suddenly standing in a spotlight with everyone looking. In one demonstration of this phenomenon, Gilovich, Medvec, and Sayitsky (2000) asked college students to put on a Barry Manilow T-shirt that fellow students had previously judged to be embarrassing. The participants were then led into a room in which other students were already participating in an experiment. After a few minutes, the participant was led back out of the room and was allowed to remove the shirt. Later, each participant was asked to estimate how many people in the room had noticed the shirt. The individuals who were in the room were also asked whether they noticed the shirt. In the study, the participants significantly overestimated the actual number of people who had noticed. a. In a similar study using a sample of n=9 participants, the individuals who wore the shirt produced an average estimate of M=6.4 with SS=162 . The average number who said they noticed was 3.1. Is the estimate from the participants significantly different from the actual number? Test the null hypothesis that the true mean is =3.1 using a two-tailed test with =.05. h. Is the estimate from the participants significantly higher than the actual number ( =3.1 )? Use a one-tailed test with =.05.]14. Many animals, including humans, tend to avoid direct eye contact and even patterns that look like eyes. Some insects, including moths, have evolved eye-spot patterns on their wings to help ward off predators. Scaife (1976) reports a study examining how eye-spot patterns affect the behaviour of birds. In the study, the birds were tested in a box with two chambers and were free to move from one chamber to another. In one chamber, two large eye-spots were painted on one wall. The other chamber had plain walls. The researcher recorded the amount of time each bird spent in the plain chamber during a 60-minute session. Suppose the study produced a mean of M=34.5 minutes on the plain chamber with SS=210 for a sample of n=15 birds. (Now: If the eye spots have no effect. then the birds should spend an average of =30 minutes in each chamber.) a. Is this sample sufficient to conclude that the eyes pots have a significant influence on the bird’s behaviour? Ike a two-tailed test with =.05. b. Compute the estimated Cohen’s d to measure the size of the treatment effect. c. Construct the 90% confidence interval to estimate the mean amount of time spent on the plain side for the population of birds.Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was =15.1 . A sample of n=16 of today’s children produces a mean score of M=23.3 with SS=240 . a. Based on the sample, has there been a significant change in the average level of anxiety since the 1950s? Use a two-tailed test with =.01 . b. Make a 90% confidence interval estimate of today’s population mean level of anxiety. c. Write a sentence that demonstrates bow the outcome of the hypothesis test and the confidence interval would appear in a research report.Weinstein, McDermott, and Roediger (2010) report that students who were given questions to be answered while studying new material had better scores when tested on the material compared to students who were simply given an opportunity to reread the material. In a similar study, an instructor in a large psychology class gave one group of students questions to be answered while studying for the final exam. The overall average for the exam was =73.4 but the n=16 students who answered questions had a mean of M=78.3 with a standard deviation of =8.4 . For this study, did answering questions while studying produce significantly higher exam scores? Use a one- tailed test with =.01 .Ackerman and Goldsmith (2011) found that students who studied text from printed hardcopy had letter test scores than students who studied from text presented on a screen. In a related study, a professor noticed that several students in a large class had purchased the c-book version of the course textbook. For the final exam, the overall average for the entire class was =81.7 but the n=9 students who used e-books had a mean of M=77.2 with a standard deviation of s=5.7 . a. Is the sample sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class? Use a two-tailed test with =.05 . b. Construct the 90% confidence interval to estimate the mean exam score if the entire population used e-books. c. Write a sentence demonstrating how the results from the hypothesis test and the confidence interval would appear in a research report.A random sample of n=16 scores is obtained from a population with a mean of =45 . After a treatment is administered to the individuals in the sample, the sample mean is found to be M=49.2 . a. Assuming that the sample standard deviation is s=8 , computer r2 and the estimated Cohen’s d to measure the size of the treatment effect. b. Assuming that the sample standard deviation is s=20 . computer r2 and the estimated Cohen’s d to measure the size of the treatment effect. c. Comparing your answers from parts a and b, how does the variability of the scores in the sample influence the measures of effect size?A random sample is obtained from a population with a mean of =45 . After a treatment is administered to the individuals in the sample, the sample mean is M=49 with a standard deviation of s=12 . a. Assuming that the sample consists of n=9 scores, compute, r2 and the estimated Cohen’s d to measure the site of treatment effect. b. Assuming that the sample consists of n=16 scores, compute r2 and the estimated Cohen’s d to measure the size of treatment effect. c. Comparing your answers from parts a and b, how does the number of scores in the sample influence the measures of effect size?An example of the vertical-horizontal illusion is shown in the figure. Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength of this illusion, a researcher prepared an example in which both lines were exactly 10 inches long. The example was shown to individual participants who were told that the horizontal line was 10 inches long and then were asked to estimate the length of the vertical line. For a sample of n=25 participants, the average estimate was M=12.2 inches with a standard deviation of s=1.00 . a. Use a one-tailed hypothesis test with =.01 to demonstrate that the individuals in the sample significantly overestimate the true length of the line. (Note: Accurate estimation would produce a mean of =10 inches.) b. Calculate the estimated d and r2 , the percentage of variance accounted for, to measure the size of this effect. c. Construct a 95% confidence interval for the population mean estimated length of the vertical line.In the Preview for this Chapter, we discussed a study by McGee and Shevlin (2009) demonstrating that an individual’s sense of humor had a significant effect on how the individual was perceived by others. In one pan of the study, female college students were given brief descriptions of a potential romantic partner. The fictitious male was described positively and, for one group of participants, the description also said that he had a great sense of humor. Another group of female students read the same description except it now said that he has no sense of humor. After reading the description, each participant was asked to rate the attractiveness of the man on a seven-point scale from 1 (very unattractive) to 7 (very attractive) with a score of 4 indicating a neutral rating. a. The females who read the “great sense of humor” description gave the potential partner an average attractiveness score of M=4.53 with a standard deviation of S=1.04 . If the sample consisted of n=16 participants, is the average rating significantly higher than neutral ( =4)? Use a one- tailed test with =.05. h. The females who read the description saying “no sense of humor” gave the potential partner an average attractiveness score of M=3.30 with a standard deviation of S=1.18 . If the sample consisted of n=16 participants, is the average rating significantly lower than neutral ( =4 )? Use a one-tailed test with =.05.Oishi and Schimmk (2010) report that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. To further examine this relationship, a psychologist obtains a sample of n=12 young adults who each experienced 5 or more different homes before they were 16 years old. These participants were given a standardized well-being questionnaire for which the general population has an average score of =40 . The well-being scores for this sample are as follows: , 37, 41, 35, 42, 40, 33, 33, 36, 38, 32, 39. a. On the basis of this sample, is well-being for frequent movers significantly different from wellbeing in the general population? Use a two-tailed test with =.05 . b. Compute the estimated Cohen’s d to measure the size of the difference. c. Write a sentence showing how the outcome of the hypothesis test and the measure of effect size would appear in a research report.Research examining the effects of preschool childcare has found that children who spent time in day care, especially high-quality day care, perform better on math and language tests than children who stay home with their mothers (Broberg, Wessels, Lamb, =50 . The scores for the sample are as follows: 57. 61.49. 52. 56. 58.62. 51. 56. a. Is this sample sufficient to conclude that the children with a history of preschool day care are significantly different from the general population? Use two-tailed test with =.01 . b. Compute Cohen’s d to measure the size of the preschool effect. c. Write a sentence showing how the outcome of the hypothesis lest and the measure of effect size would appear in a research report.Describe the basic characteristics of an independent-measures, or a between subjects, research study.Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic.One sample has SS=36 and a second sample has SS=18 . a. If n=4 for both samples, find each of the sample variances and compute the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances. b. Now assume that n=4 for the first sample and n=7 for the second. Again, calculate the two sample variances and the pooled variance. You should find that the pooled variance is closer to the variance for the larger sample.One sample has SS=60 and a second sample has SS=48 . a. If n=7 for both samples, find each of the sample variances, and calculate the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances. b. Now assume that n=7 for the first sample and n=5 for the second. Again, calculate the two sample variances and the pooled variance. You should find that the pooled variance is closer to the variance for the larger sample.] 5. Two separate samples, each with n=15 individuals, receive different treatments. After treatment, the first sample has SS=1740 and the second has SS=1620 . a. Find the pooled variance for the two samples. b. Compute the estimated standard error for the sample mean difference. c. If the sample mean difference is 8 points, is this enough to reject the null hypothesis and conclude that there is a significant difference for a two-tailed test at the .05 level?Two separate samples receive different treatments. After treatment, the first sample has n=9 with SS=462 , and the second has n=7 with SS=420 . a. Compute the pooled variance for the two samples. b. Calculate the estimated standard error for the sample mean difference. c. If the sample mean difference is 10 points, is this enough to reject the null hypothesis using a two-tailed test with =.05 ?Research results suggest a relationship between the TV viewing habits of 5-year-old children and their future performance in high school. For example, Anderson, Huston, Wright, and Collins (1998) report that high school students who regularly watched Sesame Street as children had better grades in high school than their peers who did not watch Sesame Street. Suppose that a researcher intends to examine this phenomenon using a sample of 20 high school students. The researcher first surveys the students’ parents to obtain information on the family’s TV viewing habits during the time that the students were 5 years old. Based on the survey results, the researcher selects a sample of n=10 students with a history of watching “Sesame Street” and a sample of n=10 students who did not watch the program. The average high school grade is recorded for each student and the data are as follows: Average High School Grade Watched Sesame Street Did Not Watch Sesame Street 86 99 90 79 87 97 89 83 91 94 82 86 97 89 83 81 98 92 85 92 n=10 M=93 SS=200 n=10 M=85 SS=160 Use an independent-measures t test with =.01 to determine whether there is a significant difference between the two types of high school student.It appears that there is some truth to the old adage ‘That which doesn’t kill us makes us stronger.” Seery, Holman, and Silver (2010) found that individuals with some history of adversity report better mental health and higher well-being compared to people with little or no history of adversity. In an attempt to examine this phenomenon, a researcher surveys a group of college students to determine the negative life events that they experienced in the past 5 years and their current feeling of well-being. For n=18 participants with 2 or fewer negative experiences, the average well-being score is M=42 with SS=398, and for n=16 participants with 5 to 10 negative experiences the average score is M=48.6 with SS=370 . a. Is there a significant difference between the two populations represented by these two samples? Use a two-tailed test with =.01 . b. Compute Cohen’s d to measure the size of the effect. c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.Does posting calorie content for menu items affect people’s choices in fast food restaurants? According to results obtained by Elbel, Gyamfi, and Kersh (2011), the answer is no. The researchers monitored the calorie content of food purchases for children and adolescents in four large fast food chains before and after mandatory labelling began in New York City. Although most of the adolescents reported noticing the calorie labels, apparently the labels had no effect on their choices. Data similar to the results obtained show an average of M=786 calories per meal with s=85 for n=100 children and adolescents before the labeling, compared to an average of M=772 calories with s=91 for a similar sample of n=100 after the mandatory posting. a. Use a two-tailed test with =.05 to determine whether the mean number of calories after the posting is significantly different than before calorie content was posted. b. Calculate r2 to measure effect size for the mean difference.In 1974, Loftus and Palmer conducted a classic study demonstrating how the language used to ask a question can influence eyewitness memory. In the study, college students watched a film of an automobile accident and then were asked questions about what they saw. One group was asked. “About how fast were the cars going when they smashed into each other?” Another group was asked the same question except the verb was changed to “hit” instead of “smashed into.” The “smashed into” group reported significantly higher estimates of speed than the “hit” group. Suppose a researcher repeats this study with a sample of today’s college students and obtains the following results. Estimated Speed Smashed into Hit n=15 n=15 M=40.8 M=34.0 SS=510 SS=414 a. Do the results indicate a significantly higher estimated speed for the “smashed into” group? Use a one-tailed test with =.01 . b. Compute the estimated value for Cohen’s d to measure the size of the effect. c. Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size would appear in a research report.Recent research has shown that creative people are more likely to cheat than their less creative counterparts (Gino and Andy, 2012). Participants in the study first completed creativity assessment questionnaires and then returned to the lab several days later for a series of tasks. One task was a multiple-choice general knowledge test for which the participants circled their answers on the test sheet. Afterward, they were asked to transfer their answers to a bubble sheets for computer scoring. However, the experimenter admitted that the wrong bubble sheet had been copied so that the correct answers were still faintly visible. Thus, the participants had an opportunity to cheat and inflate their test scores. Higher scores were valuable because participants were paid based on the number of correct answers. However, the researchers had secretly coded the original tests and the bubble sheets so that they could measure the degree of cheating for each participant. Assuming that the participants were divided into two groups based on their creativity scores, the following data are similar to the cheating scores obtained in the study. High Creativity Participants Low Creativity Participants n=27 n=27 M=7.41 M=4.78 SS=749.5 SS=830 a. Use a one-tailed test with =.05 to determine whether these data are sufficient to conclude that high creativity people are more likely to cheat than people with lower levels of creativity. b. Compute Cohen’s d to measure the size of the effect. c. Write a sentence demonstrating how (he results from the hypothesis test and the measure of effect size would appear in a research report.Recent research has demonstrated that music-based physical training for elderly people can improve balance, walking efficiency, and reduce the risk of falls (Trombetti et at., 2011). As part of the training, participants walked in time to music and responded to changes in the music’s rhythm during a 1-hour per week exercise program. After 6 months, participants in the training group increased their walking speed and their stride length compared to individuals in the control group. The following data are similar to the results obtained in the study. Exercise Group Stride Length Control Group Stride Length 24 25 22 24 26 23 20 23 26 17 21 22 20 16 21 17 22 19 24 23 18 23 16 20 23 28 25 23 25 19 17 16 Do the results indicate a significant difference in the stride length for the two groups? Use a two-tailed test with =.05 .McAllister et al. (2012) compared varsity football and hockey players with varsity athletes from noncontact sports to determine whether exposure to head impacts during one season have an effect on cognitive performance. In the study, tests of new learning performance were significantly poorer for the contact sport athletes compared to the noncontact sport athletes. The following table presents data similar to the results obtained in the study. Noncontact Athletes Contact Athletes 10 7 8 4 7 9 9 3 13 7 7 6 6 10 12 2 a. Are the test scores significantly lower for the contact sport athletes than for the noncontact athletes? Use a one-tailed test with =.05. b. Compute the value of r2 (percentage of variance accounted for) for these data.In the Chapter Preview we presented a study showing that handling money reduces the perception pain (Thou, Vohs, =.01 . b. Compute Cohen’s d to estimate the size of the treatment effect.In a classic study in the area of problem solving, Katona (1940) compared the effectiveness of two methods of instruction. One group of participants was shown the exact. step-by-step procedure for solving a problem and was required to memorize the solution. Participants in a second group were encouraged to study the problem and find the solution on their own. They were given helpful hints and clues, but the exact solution was never explained. The study included the problem in the following figure showing a pattern of five squares made of matchsticks. The problem is to change the pattern into exactly four squares by moving only three matches. (All matches must be used. none can be removed, and all the squares must be the same size.) After 3 weeks, both groups returned to be tested again. The two groups did equally well on the matchstick problem they had learned earlier. But when they were given new problems (similar to the match- stick problem), the memorization group had much lower scores than the group who explored and found the solution on their own. The following data demonstrate this result. Memorization of the Solution Find a Solution Your Own n=8 n=8 M=10.50 M=6.16 SS=108 SS=116 Incidentally, if you still have not discovered the solution to the matchstick problem, keep trying. According to Katona’s results, it would be very poor teaching strategy for us to give you the answer. If you still have not discovered the solution, however, check Appendix C at the beginning of the problem solutions for Chapter 10 and we will show you how it is done. a. Is there a significant difference in performance on new problems for these two groups? Use a two- (ailed test with =.05 . b. Construct a 90% confidence interval to estimate the size of the mean difference. n=8 A researcher conducts an independent-measures study comparing two treatments and reports the t statistic as t(25)=2.071 . a. How many individuals participated in the entire study? b. Using a two-tailed test with =.05 , is there a significant difference between the two treatments? c. Computer r2 to measure the percentage of variance accounted for by the treatment effect.In a recent study, Piff, Kraus, Côté, Cheng, and Keitner (2010) found that people from lower social economic classes tend to display greater prosocial behavior than their higher class counterparts. In one part of the study, participants played a game with an anonymous partner. Part of the game involved sharing points with the partner. The lower economic class participants were significantly more generous with their points compared with the upper class individuals. Results similar to those found in the study, show that n=12 lower class participants shared an average of M=5.2 points with SS=11.91 . compared to an average of M=4.3 with SS=9.21 for then n=12 upper class participants. a. Are the data sufficient to conclude that there is a significant mean difference between the two economic populations? Use a two-tailed test with =.05 .b. Construct an 80% confidence interval to estimate the size of the population mean difference.Describe the homogeneity of variance assumption and explain why it is important for the independent- measures ttest.If other factors are held constant, explain how each of the following influences the value of the independent- measures tstatistic, the likelihood of rejecting the null hypothesis, and the magnitude of measures of effect size. a. Increasing the number of scores in each sample. b. Increasing the variance for each sample.As noted on page 304, when the two population means are equal, the estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that 1=2 . and calculate how much difference should be expected between the two sample means. a. One sample has n=6 scores with SS=75 and the second sample has n=10 scores with SS= 135. b. One sample has n=6 scores with SS=310 and the second sample has n=10 scores with SS=530 . c. In part b, the samples have larger variability (bigger SS values) than in part a. but the sample sizes are unchanged. How does larger variability affect the magnitude of the standard error for the sample mean difference?Two samples are selected from the sane population. For each of the following, calculate how much difference is expected, on average, between the two sample means. a. One sample has n=4 , the second has n=6 , and the pooled variance is 60. b. One sample has n=12 , the second has n=15 , and the pooled variance is 60. c. In part b, the sample sizes are larger but the pooled variance is unchanged. How does larger sample size affect the magnitude of the standard error for the sample mean difference?For each of the following, assume that the two samples are obtained from populations with the same mean, and calculate how much difference should be expected, on average, between the two sample means. a. Each sample has n=4 scores with s2=68 for the first sample and s2=76 for the second. (Now: Because the two samples are the same size, the pooled variance is equal to the average of the two sample variances.) b. Each sample has n=16 scores with s2=68 for the first sample and s2=76 for the second. c. In part b. the two samples are bigger than in part a. but the variances are unchanged. How does sample Size affect the size of the standard error for the sample mean difference?For each of the following, calculate the pooled variance and the estimated standard error for the sample mean difference a. The first sample has n=4 scores and a variance of s2=17 , and the second sample has n=8 scores and a variance of s2=27 . b. Now the sample variances are increased so that the first sample has n=4 scores and a variance of s2=68 , and the second sample has n=8 scores and a variance of s2=108 . c. Comparing your answers for parts a and b, how does increased variance influence the size of the estimated standard error?For the each of the following studies determine whether a repeated-measures t test is the appropriate analysis. Explain your answers. a. A researcher is examining the effect of violent video games on behaviour by comparing aggressive behaviours for one group who just finished playing a violent game with another group who played a neutral game. b. A researcher is examining the effect on humor on memory by presenting a group of participants with a series of humorous and not humorous sentences and them recording how many of each type of sentence is recalled by each participant. c. A researcher is evaluating the effectiveness of a new cholesterol medication by recording the cholesterol level for each individual in a sample before they start taking the medication and again after 8 weeks with the medication.What is the defining characteristic of a repeated-measures or within-subjects research design?Explain the difference between a matched-subjects design and a repeated-measures design.A researcher conducts an experiment comparing two treatment conditions with 20 scores in each treatment condition. a. If an independent-measures design is used, how many subjects arc needed for the experiment? b. If a repeated-measures design is used, how many subjects are needed for the experiment? c. If a matched-subjects design is used, how many subjects arc needed for the experiment?A sample of n=9 individuals participates in a repeated-measures study that produces a sample mean difference of Md=4.25 with SS=128 for the difference scores. a. Calculate the standard deviation for the sample of difference scores. Briefly explain what is measured by the standard deviation. b. Calculate the estimated standard error for the sample mean difference. Briefly explain what is measured by the estimated standard error.In the Preview for Chapter 2, we presented a study showing that a woman shown in a photograph was judged as less attractive when the photograph showed a visible tattoo compared to the same photograph with the tattoo removed (Resenhoeft, Villa, =.05 .The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of n=6participants before and after they receive the treatment. a. Calculate the difference scores and Md. b. Compute SS. sample variance, and estimated standard error. c. Is there a significant treatment effect? Use =.05, two tails. Participant Before Treatment After Treatment A 7 8 B 2 9 C 4 6 D 5 7 E 5 6 F 3 8 When you get a surprisingly low price on a product do you assume that you got a really good deal or that you bought a low-quality product? Research indicates that you are more likely to associate low price and low quality if someone else makes the purchase rather than yourself (Yan and Sengupta, 2011). In a similar study, n=16 participants were asked to rate the quality of low-priced items under two scenarios: purchased by a friend or purchased yourself. The results produced a mean difference of Md=2.6 and SS=135 , with self-purchases rated higher. a. Is the judged quality of objects significantly different for self-purchases than for purchases made by others? Use a two-tailed test with =.05 . b. Compute Cohen’s d to measure the size of the treatment effect.Masculine-themed words (such as competitive, independent, analyze, strong) are commonly used in job recruitment materials, especially for job advertisements in male-dominated areas (Gaucher, Friesen, =.05 . b. Compute r2 to measure the size of the treatment effect. c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.The stimulant Ritalin has been shown to increase attention span and improve academic performance in children with ADHD (Evans et al., 2001). To demonstrate the effectiveness of the drug, a researcher selects a sample of n=20 children diagnosed with the disorder and measures each child’s attention span before and after taking the drug. The data show an average increase of attention span of Md=4.8 minutes with a variance of s2=125 for the sample of difference scores. a. Is this result sufficient to conclude that Ritalin significantly improves attention span? Use a one-tailed test with =.05 . b. Compute the 80% confidence interval for the mean change in attention span for the population.College athletes, especially males, are often perceived as having very little interest in the academic side of their college experience. One common problem is class attendance. To address the problem of class attendance, a group of researchers developed and demonstrated a relatively simple but effective intervention (Bicard, Lou, Mills, Bicard, =.01 to determine whether texting produced a significant change in attendance. h. Compute a 95% confidence interval to estimate the mean change in attendance for the population.Callahan (2009) demonstrated that Tai Chi can significantly reduce symptoms for individuals with arthritis. Participants were 18 years old or older with doctor- diagnosed arthritis. Self-reports of pain and stiffness were measured at the beginning of an 8-wcek Tai Chi course and again at the end. Suppose that the data produced an average decrease in pain and stiffness of Md=8.5 points with a standard deviation of 21.5 for a sample of n=40 participants. a. Use a two-tailed test with =.05 to determine whether the Tai Chi had a significant effect on pain and stiffness. b. Compute Cohen’s d to measure the size of the treatment effect.Research results indicate that physically attractive people are also perceived as being more intelligent (Eagly, Ashmore, Makhijani, =.05 .There is some evidence suggesting that you are likely to improve your test score if you rethink and change answers on a multiple-choice exam (Johnston, 1975). To examine this phenomenon, a teacher gave the same final exam to two sections of a psychology course. The students in one section were told to turn in their exams immediately after finishing, without changing any of their answers. In the other section, students were encouraged to reconsider each question and to change answers whenever they kit it was appropriate. Before the final exam, the teacher had matched 9 students in the first section with 9 students in the second section based on their midterm grades. For example, a student in the no-change section with an 89 on the midterm exam was matched with student in the change section who also had an 89 on the midterm. The difference between the two final exam grades for each matched pair was computed and the data showed that the students who were allowed to change answers scoring higher by an average of Md=7 points with SS=288 . a. Do the data indicate a significant difference between the two conditions? Use a two-tailed test with =.05. b. Construct a 95% confidence interval to estimate the size of the population mean difference. c. Write a sentence demonstrating how the results of the hypothesis test and the confidence interval would appear in a research report.Research indicates that the color red increases men’s attraction to women (Elliot and Niesta, 2008). In the original study, men were shown women’s photographs presented on either a white or a red background. Photographs presented on red were rated significantly more attractive than the same photographs mounted on white. In a similar study, a researcher prepares a set of 30 women’s photographs, with 15 mounted on a white background and 15 mounted on red. One picture is identified as the test photograph, and appears twice in the set, once on white and once on red. Each male participant looks through the entire set of photographs and rates the attractiveness of each woman on a 15-point scale. The following table summarizes the ratings of the test photograph for a sample of n=9 men. Are the ratings for the test photograph significantly different when it is presented on a red background compared to a white background? Use a two-tailed test with =.01 . Participant White Background Red Background A 4 7 B 6 7 C 5 8 D 5 9 E 6 9 F 4 7 G 3 9 H 8 9 1 6 9 Example 11.2 in this chapter presented a repeated-measures research study demonstrating that swearing can help reduce ratings of pain (Stephens, Atkins, =.05 . b. Compute r2 , the percentage of variance accounted for, to measure the size of the treatment effect. c. Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size would appear in a research report. Amount of Time (In Seconds) Participant Swear words Neutral words 1 94 59 2 70 61 3 52 47 4 83 60 5 46 35 6 117 92 7 69 53 8 39 30 9 51 56 10 73 61 a. A repeated-measures study with a sample of n=16 participants produces a mean difference of Md=3 with a standard deviation of s=4 . Use a two-tailed hypothesis test with =.05 to determine whether this sample provides evidence of a significant treatment effect. b. Now assume that the sample standard deviation is s=12 and repeat the hypothesis test. c. Explain how the size of the sample standard deviation influences the likelihood of finding a significant mean difference.a. A repeated-measures study with a sample of n=16 participants produces a mean difference of Md=4 with a standard deviation of s=4 . Use a two-tailed hypothesis test with =.05 to determine whether it is likely that this sample came from a population with d=0 . b. Now assume that the sample mean difference is Md=10 , and once again visualize the sample distribution. Use a two-tailed hypothesis test with =.05 to determine whether it is likely that this sample came from a population with d=0 . c. Explain how the size of the sample mean difference influences the likelihood of finding a significant mean difference.A sample of difference scores from a repeated-measures experiment has a mean of Md=3 with a standard deviation of s=4 . a. If n=4 , is this sample sufficient to reject the null hypothesis using a two-tailed test with =.05 ? b. Would you reject H0 if n=16 ? Again, assume a two-tailed test with =.05 . c. Explain how the size of the sample influences the likelihood of finding a significant mean difference.Participants enter a research study with unique characteristics that produce different scores from one person to another. For an independent-measures study, these individual differences can cause problems. Identify the problems and briefly explain how they are eliminated or reduced with a repeated-measures study.In the Chapter Preview we described a study showing that students had more academic problems following nights with less than average sleep compared to nights with more than average sleep (Gillcn-O’Neel. Huynh, =.05 , is there a significant difference between the two sets of scores? b. Now assume that the data are from a repeated-measures study using the same sample of is n=8 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference and the repealed-measures t statistic. Using a two-tailed test with =.05 , is there a significant difference between the two sets of scores? (You should find that the repeated-measures design substantially reduces the variance and increases the likelihood of rejecting H0 .) n=8 n=8 22. The previous problem demonstrates that removing individual differences can substantially reduce variance and lower the standard error. However, this benefit only occurs if the individual differences are consistent across treatment conditions. In problem 21, for example, the participants with the highest scores in the more-sleep condition also had the highest scores in the less-sleep condition. Similarly, participants with the lowest scores in the first condition also had the lowest scores in the second condition. To construct the following data, we started with the scores in problem 21 and scrambled the scores in treatment 1 to eliminate the Consistency of the individual differences. Number of Academic Problems Student Following Nights with Above Average Sleep Following Nights with Below Average Sleep A 10 13 B 8 14 C 5 13 D 5 5 E 4 9 F 10 6 G 11 6 II 3 6 a. Treat the data as if the scores are from an independent-measures study using two separate samples, each with n=8 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using a two-tailed test with =.05 , is there a significant difference between the two sets of scores? Note: The scores in each treatment are the same as in Problem 21. Nothing has changed. b. Now assume that the data are from a repeated-measures study using the same sample of n=8 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference and the repeated-measures K statistic. Using a two-tailed test with =.05 , is there a significant difference between the two sets of scores? (You should find that removing the individual differences with a repeated-measures t no longer reduces the variance because there are no consistent individual differences.)Explain why the F-ratio is expected to be near 1.00 when the null hypothesis is true.Describe the similarities between an F-ratio and a t statistic.Why should you use ANOVA instead of several ttests to evaluate mean differences when an experiment consists of three or more treatment conditions?Calculate SStotal , SSbetween , and SSwithin for the following set of data: Treatment 1 Treatment 2 Treatment 3 n=10 n=10 n=10 N=30 T=10 T=20 T=30 G=60 SS=27 SS=16 SS=23 X2=206 A researcher uses an ANOVA to compare three treatment conditions with a sample of n=8 in each treatment. For this analysis, find dftotal , dfbetween , and dfwithin .A researcher reports an F-ratio with dfbetween=2 and dfwithin=30 for an independent-measures ANOVA. a. How many treatment conditions were compared in the experiment? b. How many subjects participated in the experiment?A researcher reports an F-ratio with df=2,27 from an independent-measures research study. a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study?A research report from an independent-measures study states that there are significant differences between treatments. F(3,48)=2.95,p.05. a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study?Treatment I II III n=10 n=10 n=10 SS=63 SS=66 SS=87 9. The following values are from an independent-measures study comparing three treatment conditions. a. Compute the variance for each sample. b. Compute MSwithin , which would be the denominator of the F-ratio for an ANOVA. Because the samples are all the same size, you should find that MSwithin is equal to the average of the three sample variances.A researcher conducts an experiment comparing four treatment conditions with a separate sample of n=6 in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the following table. Complete all missing values in the table. (Hint: Begin with the values in the df column. Source SS df MS Between treatments ___ ___ ___ F = ___ Within treatments ___ ___ 2 Total 58 ___The following summary table presents the results from an ANOVA comparing four treatment conditions with n=10 participants in each condition. Complete all missing values. (Hint: Start with the df column.) Source SS df MS Between treatments ___ ___ 10 F = ___ Within treatments ___ ___ ___ Total 174 ___A developmental psychologist is examining the development of language skills from age 2 to age 4. Three different groups of children are obtained, one for each age, with n=18 children in each group. Each child is given a language-skills assessment test. The resulting data were analyzed with an ANOVA to test for mean differences between age groups. The results of the ANOVA are presented in the following table. Fill in all missing values. Source SS DF MS Between treatments 48 ___ ___ F = ___ Within treatments ____ ____ ___ Total 252 ____The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with =.05 to determine whether there are any significant mean differences among the treatments. Treatment I II III 5 2 7 1 6 3 2 2 2 3 3 4 0 5 5 1 3 2 2 0 4 2 3 5 The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with =.05 to determine whether there are any significant mean differences among the treatments. Treatments I II III n=8 n=6 n=4 N=18 T=16 T=24 T=32 G=72 SS=40 SS=24 SS=16 X2=464 A research study comparing three treatment conditions produces T=20 with a=4 for the first treatment. T=10 with a=5 for the second treatment, and T=30 with a=6 for the third treatment. Calculate SSbetweentreatments for these data.Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of the F-ratio would increase or decrease. a. Increase the differences between the sample means. b. Increase the sample variances.A researcher used ANOVA and computed and F-ration for the following data. Treatments I II III n=10 n=10 n=10 M=20 M=28 M=35 SS=105 SS=191 SS=180 If the mean for treatment III were changed to M=25 , what would happen to the size of the F-ratio (increase or decrease)? Explain your answer. If the SS for treatment I were changed to SS=1400 , what would happen to the size of the F-ratio (increase or decrease)? Explain your answer.The following data were obtained from an independent-measures study comparing three treatment conditions. Treatments I II III 4 3 8 N=12 3 1 4 G=48 5 3 6 X2=238 4 1 6 M=4 M=2 M=6 T=16 T=8 T=24 SS=2 SS=4 SS=8 Calculate the sample variance for each of the three samples. Use an ANOVA with =.05 to determine whether there are any significant differences among the three treatment means.For the preceding problem you should find that that there are significant differences among the three treatments. One reason for the significance is that the sample variances are relatively small. To create the following data, we kept the same sample means that appeared in problem 8 but increased the SS values within each sample. Treatments I II III 4 4 9 N=12 2 0 3 G=48 6 3 6 X2=260 4 1 6 M=4 M=2 M=6 T=16 T=8 T=24 SS=8 SS=10 SS=18 Calculate the sample variance for each of the three samples. Describe how these samples variances compare with those from problem 8. Predict how the increase in sample variance should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the value obtained in problem 8? Use an ANOVA with =.05 to determine whether there are any significant differences among the three treatment means. (Does your answer agree with your prediction in part b?)The following data summarize the results from an independent-measures study comparing three treatment conditions. M=2 M=3 M=4 n=10 n=10 n=10 T=20 T=30 T=40 s2=2.67 s2=2.00 s2=1.33 a. Use an ANOVA with =.05to determine whether there are any significant differences among the three treatment means. Note: Because the samples are all the same size. MSwithin is the average of the three sample variances. b. Calculate 2 to measure the effect size for this study.To create the following data we started with the sane sample means and variances that appeared in problem 20 but increased the sample size to n=25 . M=2 M=3 M=4 n=25 n=25 n=25 T=50 T=75 T=100 s2=2.67 s2=2.00 s2=1.33 a. Predict how the increase in sample size should affect the F-ratio for these data compared to the F ratio in problem 20. Use an ANOVA to check your prediction. Note: Because the samples are all the same size, MSwithinis the average of the three sample variances. b. Predict how the increase in sample size should affect the value of 2 for these data compared to the 2 in problem 10. Calculate 2 to check your prediction.The following values are from an independent- measures study comparing three treatment conditions. Treatment I II III n=8 n=8 n=8 SS=42 SS=28 SS=98 a. Compute the variance for each sample. b. Compute which would be the denominator of the F-ratio for an ANOVA. Because the samples are all the same size, you should find the MSwithin is equal to the average of the three sample variances.An ANOVA produces an F-ratio with df=1,34 . Could the data have been analyzed with a t test? What would be the degrees of freedom for the t statistic?The following scores are from an independent-measures study comparing two treatment conditions. a. Use an independent-measures t test with =.05 to determine whether there is a significant mean difference between the two treatments. b. Use an ANOVA with =.05 to determine whether there is a significant mean difference between the two treatments. You should find that F=t2 . Treatment I II 1 12 6 5 N=8 6 6 G=48 3 9 X2=368 How does the denominator of the F-ratio (the error term) for a repeated-measures ANOVA compare to the denominator for an independent-measures ANOVA?The repeated-measures ANOVA can be viewed as a two-stage process. What is the purpose for the second stage?A researcher conducts an experiment comparing four treatment conditions with n=12 scores in each condition. a. If the researcher uses an independent-measures design, how many individuals are needed for the study and what are the df values for the F-ratio? b. If the researcher uses a repeated-measures design. how many individuals are needed for the study and what are the df values for the F-ratio?A researcher conducts a repeated-measures experiment using a sample of n=15 subjects to evaluate the differences among three treatment conditions. If the results are examined with an ANOVA. what are the df values for the F-ratio?The following data were obtained from a repeated- measures study comparing three treatment conditions. Use a repeated-measures ANOVA with =.05 to determine whether there are significant mean differences among the three treatments. Treatments Person I II III Person Totals A 0 2 4 P=6 B 0 3 6 P=9 N=15 C 3 7 8 P=18 G=60 D 4 1 6 P=12 X2=350 E 2 6 7 P=15 M=1 M=5 M=6 T=5 T=25 T=30 SS=8 SS=22 SS=10 The following data represent the results of a repeated- measures study comparing different viewing distances for a 42-inch high-definition television. Four viewing distances were evaluated, 9 feet, 12 feet, 15 feet. and 18 feet. Each participant was free to move back and forth among the four distances while watching a 30-minute video on the television. The only restriction was that each person had to spend at least 2 minutes watching from each of the four distances. At the end of the video, each participant rated the all of the viewing distances on a scale from 1 (Very Bad, definitely need to move closer or farther away) to 7 (excellent, perfect viewing distance). a. Use a repealed-measures ANOVA with =.05 to determine whether there are significant difference among the low viewing distances. b. Compute 2 to measure the size of the treatment effect. Viewing Distance Person 9 Feet 12 Feet 15 Feet 18 Feet Person Totals A 3 4 7 6 P=20 n=5 B 0 3 6 3 P=12 k=4 C 2 1 5 4 P=12 N=20 D 0 1 4 3 P=8 G=60 E 0 1 3 4 P=8 X2=262 T=5 T=10 T=25 T=20 SS=8 SS=8 SS=10 SS=6 The following data were obtained from a repeated- measures study comparing two treatment conditions. Use a repeated-measures ANOVA with =.05 to determine whether there are significant mean differences between the two treatments. Treatments Person I II Person Totals A 3 5 P=18 B 5 9 P=14 N=16 C 1 5 P=6 G=80 D 1 7 P=8 X2=500 E 5 9 P=14 F 3 7 P=10 G 2 6 P=8 H 4 8 P=12 M=3 M=7 T=24 T=56 SS=18 SS=18 The following data were obtained from a repeated- measures study comparing three treatment conditions. a. Use a repeated-measures ANOVA with =.05to determine whether there are significant mean differences among the three treatments. b. Compute 2 , the percentage of variance accounted for by the mean differences, to measures the size of the treatment effects. c. Write a sentence demonstrating how a research report would present the results of the hypothesis test and the measure of effect size. Treatments Person I II III Person Totals A 1 1 4 P=6 B 3 4 8 P=15 N=15 C 0 2 7 P=9 G=45 D 0 0 6 P=6 X2=231 E 1 3 5 P=9 M=1 M=2 M=6 T=5 T=10 T=30 SS=6 SS=10 SS=10 For the data in problem 8, a. Compute SStotal and SSbetweentreatments . b. Eliminate the mean difference between treatments by adding 2 points to each score in treatment I, adding 1 point to each score in treatment II, and subtracting 3 points from each score in treatment II. (All three treatments should end up with M=3 and T=15 .) c. Calculate SStotal for the modified scores. (Caution: You first must find the new value for X2 .) d. Because the treatment effects were eliminated in part b, you should find that SStotal for the modified scores is smaller than SStotal for the original scores. The difference between the two SS values should be exactly equal to the value of SSbetweentreatments for the original scores.In the Preview section for this chapter, we presented an example of a delayed discounting study in which people are willing to settle for a smaller reward today in exchange for a larger reward in the future. The following data represent the typical results from one of these studies. The participants are asked how much they would take today instead of waiting for a specific delay period to receive $1000. Each participant responds to all 5 of the delay periods. Use a repeated-measures ANOVA with =.01 to determine whether there are significant differences among the 5 delay periods for the following data: Participant 1 month 6 months 1 year 2 years 5 years A 950 850 800 700 550 B 800 800 750 700 600 C 850 750 650 600 500 D 750 700 700 650 550 E 950 900 850 800 650 F 900 900 850 750 650 The endorphins released by the brain act as natural painkillers. For example, Gintzler (1970) monitored endorphin activity and pain thresholds in pregnant rats during the days before they gave birth. The data showed an increase in pain threshold as the pregnancy progressed. The change was gradual until 1 or 2 days before birth, at which point there was an abrupt increase in pain threshold. Apparently a natural painkilling mechanism was preparing the animals for the stress of giving birth. The following data represent pain-threshold scores similar to the results obtained by Gintzler. Do these data indicate a significant change in pain threshold? Use a repeated-measures ANOVA with =.01 . Day Before Giving Birth Subject 7 5 3 1 A 39 40 49 52 B 38 39 44 55 C 44 46 50 60 D 40 42 46 56 E 34 33 41 52 A researcher is evaluating customer satisfaction with the service and coverage of two phone carriers. Each individual in a sample of n = 16 uses one carrier for two weeks and then switches to the other. Each participant then rates two carriers. The following table presents the results from the repeated-measures ANOVA comparing the average ratings. Fill in the missing values in the table. (Hint:: Start with the df values.) Source SS df MS Between 8 F = treatments Within treatments Error 60 Total 103 The following summary table presents the results from a repealed-measures ANOVA comparing three treatment conditions with a sample of n=8 participants. Fill in the missing values in the table. (Hint: Sian with the df values.) Source SS df MS Between treatments F=6.50 Within treatments 70 Between subjects Error 28 Total The following summary table presents the results from a repeated-measures ANOVA comparing four treatment conditions, each with a sample of n=20 participants. Fill in the missing values in the table. (Hint: Start with the df values.) Source SS df MS Between treatments 33 F = Within treatments Between subjects Error 3 Total 263

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