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

A researcher is interested in the fast-food eating habits of American college students. A group of 50 students is interviewed and the researcher finds that these students eat an average of 2.3 commercially prepared meals per week. For this study, the average of 2.3 meals is an example of a ______. a. parameter b. statistic c. population d. sampleA researcher is curious about the average distance traveled by Canada geese during peak fall migration in the state of New York. The entire group of Canada geese in the state is an example of a_______. a. sample b. statistic c. population d. parameterWhat term is used for the statistical techniques that use sample data to draw conclusions about the population from which the sample was obtained? a. population statistics b. sample statistics c. descriptive statistics d. inferential statisticsThe SAT is standardized so that the average score on the verbal test is 500 each year. If you select a group of 100 graduating seniors who have taken the verbal SAT, what value would be obtained for their average score? a. 500 b. greater than 500 c. less than 500 d. around 500 but probably not equal to 5001LCA researcher studies the factors that determine the number of jobs adults have in a lifetime. The variable, number of jobs, is an example of a(n) ______ variable. a. discrete b. continuous c. nominal d. ordinalWhen measuring height to the nearest half inch, what are the real limits for a score of 69.0 inches? a. 68 and 70 b. 68.5 and 69.5 c. 68.75 and 69.75 d. 68.75 and 69.25Ranking a group of cities in terms of "quality of life" would be an example of measurement on a(n)______scale of measurement. a. nominal b. ordinal c. interval d. ratioIn a correlational study, how many variables are measured for each individual and how many groups of individuals are in the study? a. One variable and one group b. One variable and two groups c. Two variables and one group d. Two variables and two groupsA research study comparing alcohol use for college students in the United States and Canada reports that more Canadian students drink but American students drink more (Kuo, Adlaf, Lee. Gliksman, Demers, Wechsler. 2002).What research design did this study use? a. Correlational b. Experimental c. Nonexperimental d. NoncorrelationalA recent study reports that infant rats fed a diet containing genetically modified grains reached an adult weight 10% greater than their litter-mates raised on a regular diet. For this study, what is the independent variable? a. The rats given the genetically modified diet b. The rats given the regular diet c. The type of diet given to the rats d. The adult weight of the ratsWhat value is represented by the uppercase letter N? a. the number of scores in a population b. the number of scores in a sample c. the number of values to be added in a summation problem d. the number of steps in a summation problemWhat is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16What is the last step in the calculation of (X)2? a. Square each score. b. Add the scores. c. Square the sum of the scores d. Add the squared scores.A researcher is 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 messages that each individual sends each day, and calculates the average number for the group. a. Identify the population for this study. b. Identify the sample for this study. c. The average number that the researcher calculated is an example of a_______.Define the terms population and sample, and explain the role of each in a research study.Statistical methods arc classified into two major categories: descriptive and inferential. Describe the general purpose for the statistical methods in each category.Define the terms statistic and parameter and explain how these terms are related to the concept of sampling error.Explain why honesty is a hypothetical construct instead of a concrete variable. Describe how honesty might be measured and defined using an operational definition.A lax form asks people to identify their age. 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 identity whether the variable is continuous or discrete.Four scales of measurement were introduced in this chapter, from simple classification on a nominal scale to the more informative measurements from a ratio scale. 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 measurement 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?Describe the data for a correlation research study and 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.The results of a recent study showed that children who routinely drank reduced fat milk (1% or skim) were more likely to be overweight or obese at ages 2 and 4 compared to children who drank whole or 2% milk (Scharf, Demmer, DeBoer, 2013). Is this an example of an experimental or a nonexperimental study?Gentile, Lynch, Linder, and Walsh (2004) surveyed over 600 eighth-and ninth-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.A research study comparing alcohol use for college students in the United States and Canada reports that more Canadian students drink but American students drink more (Kuo, Adlaf, Lee, Gliksman, Demers, Wechsler, 2002). Is this study an example of an experiment? Explain why or why not.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.Ackerman and Goldsmith (2011) compared learning performance for students who studied material printed on paper versus students who studied the same material presented on a computer screen. All students were then given a test on the material and the researchers recorded the number of correct answer. 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?There is some evidence that people with a visible tattoo are considered to be less attractive than are people without a visible tattoo. Resenhoeft, Villa, and Wiseman (2008) showed one group of students a color photograph of a 24-year-old woman with a tattoo of a dragon on her arm. A second group of students was shown the same photograph but with the tattoo removed. Each participant was asked to rate the attractiveness of the woman in the photograph. 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?Guguen and Jacob (2012) asked waitresses to wear different colored T-shirts on different days for a six-week period and recorded the lips left by male customers. The results show that male customers gave significantly bigger tips to waitresses when they were wearing red. For this study, identify the independent variable and the dependent variable.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 bums 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?For the following scores, find the value of each expression: X 3 2 4 2 a. X b. (X)2 c. X 2 d. (X 2)For the following set of scores, find the value of each expression: X 1 2 4 1 3 a. X2 b. (X)2 c. (X + 1) d. (X + 1)2For the following set of scores, find the value of each expression: a. X b. (X)2 c. X2 d. (X +3)Two scores, X and Y, are recorded for each of n = 5 participants. For these scores, find the value of each expression. a. X b. Y c. (X + Y) d. XY Subject X Y A 3 1 B 1 5 C 2 2 D 4 2 E 2 4Use summation notation lo express each of the following calculations a. Add the scores and 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.For the following set of stores, find the value of each expression: a. X b. (X) c. (X 3) d. (X 3) X 4 5 2 1 3If the following scores are placed in a frequency distribution table, then what is the frequency value corresponding to X = 2? Scores: 2, 3, 1, 1, 3, 3, 2, 4, 3, 1 a. 1 b. 2 c. 3 d. 4For the following distribution of quiz scores, how many individuals took the quiz? x f 5 6 4 5 3 5 2 3 1 2 a. 5 b. 10 c. 15 d. 21For the following frequency distribution, what is the value of X? x f 5 1 4 0 3 2 2 2 1 3 a. 50 b. 55 c. 74 d. 225A set of scores ranges from a high of X = 96 to a low of X = 27. If these scores are placed in a grouped frequency distribution table with an interval width of 10 points, the top interval in the table would be ___________. a. 9099 b. 90100 c. 91100 d. 8796What is the lowest score in the following distribution?Which of the following statements is false regarding grouped frequency distribution tables? a. An interval width should be used that yields about 10 intervals. b. Intervals are listed in descending order, starting with the highest value at the top of the X column. c. The bottom score for each interval is a multiple of the interval width. d. The value for N can be determined by counting the number of intervals in the X columnWhich of the following measuring scales are displayed by frequency distribution polygons? a. Either interval or ratio scales b. Only ratio scales c. Either nominal or ordinal scales d. Only nominal scalesA group of quiz, scares, is shown in a histogram If the bars in the histogram gradually decrease in height from left to right, what can you conclude about the set of quiz scores? a. There are more high scores than there are low scores. b. There are more low scores than there are high scores. c. The height of the bars always decreases as the scores increase. d. None of the above.Instead of showing the actual number of individuals in each category, a population frequency distribution graph usually shows a(n)________. a. estimated frequency b. grouped frequency c. relative frequency d. hypothetical frequencyIn a distribution with positive skew, where are the scoreswith the highest frequencies located? a. On the right side of the distribution b. On the left side of the distribution c. In the middle of the. distribution d. Represented at two distinct peaksPlace the following set of n = 20 scores in a frequency distribution table.Construct a frequency distribution table for the following set of scores. Include columns for proportion and percentage in your table.Find each value requested for the distribution of scores in the following table. a. n b. X c. X2 X f 5 2 4 3 3 1 2 4 1 2For each of the following, determine the interval width that would be best for a grouped frequency distribution and identify the approximate number of intervals needed to cover the range of scores. a. Scores that range from X = 6 In X = 81 b. Scores that range from X = 18 to X= 34 c. Scores that range from X = 56 to X = 97For the following scores, the smallest value is X 7 and the largest value is X 48. a. Determine the best interval width and identify the approximate number of intervals needed for u grouped frequency distribution table. b. It Place the scores in a grouped frequency distribution table using the interval width you determined.The following scores are the ages for a random sample of n = 32 drivers who were issued parking tickets in Chicago during 2015. 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 usual equally across age groups?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 at scores: 1. Construct a frequency distribution table to organize the scores. 2. Draw a frequency distribution histogram for these dataDraw a histogram for the distribution of scores shown in the following table. x f 10 2 9 4 8 1 7 1 6 4 5 2Draw a polygon for the distribution of scores shown in the following table. X f 6 2 5 5 4 3 3 2 2 1For the following set or scores: a. Organize the scores in a frequency distribution table. b. Based on the frequencies, identify the shape of the distribution.Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of the distribution?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. age b. birth-order position among siblings (oldest - first) c. academic major d. registered voter (yes/no)Gaucher, Friesen, and Kay (2011) found that words they identified as masculine themed (such tut 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 advertisement 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 or the followin.tt values for the distribution shown in the following polygon. a. n b. X c. X2For the following set of scores: a. Construct a frequency distribution table. b. Sketch a histogram showing the distribution. c. Describe the distribution using the following characteristics: (1) What is the shape of the distribution? (2) What score best identities the center (average) for the distribution? (3) Are the scores clustered together, or are they spread out across the scale?A local fast-food restaurant normally sells coffee in three sizes- small, medium, and large-at three different prices. Recently they had a special sale, charging only SI for any sized coffee. During the sale, an employee recorded the number of each coffee size that was purchased on Wednesday morning. The following Wednesday, when prices had returned to normal, she again recorded the number of coffees sold for each Size. The results are shown in the following table. Regular Prices x f Large 12 Medium 25 Small 31 All Sizes for 1 X f Large 41 Medium 27 Small 11 a. What kind of graph would be appropriate for showing the distribution of coffee sizes for each of the two time periods? b. Draw the two frequency distribution graphs. c. Based on your two graphs, did the sale have an influence on the size of coffee that customers ordered?Weinstein, McDermott, and Roediger (2010) published an experimental study examining different techniques that students use to prepare for a test. Students read a passage, knowing that they would have a quiz on the material. After reading the passage, students in one condition were asked to continue studying by s imply reading the passage again. In a second condition, students answered a series of prepared questions about the material. Then all students took the Quiz. The following table shows quiz scores similar to the results obtained in the study. Quiz Scores for Two Groups of Students Simply Reread Answer Questions B, 5, 7, 9, 8 9, 7, 8, 9, 9 9, 9, 8, 6, 9 8, 10, 9, 5, 10 7, 7, 4, 6, 5 7, 8, 7, 8 Sketch a polygon showing the frequency distribution for students who reread the passage. In the same graph, sketch a polygon showing the scores for the students who answered questions. (Use two different colors or use a solid line for one polygon and a dashed line for the other.) Does it look like there is a difference between the two groups?Recent research suggests that the amount of lime 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 childrens homes between the ages of 14 and 30 months and recorded the amount of number talk they heard from the childrens parents. The researchers then tested the childrens knowledge of the meaning of numbers at 46 months. The following data are similar to the results obtained in the study. Childrens 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?A sample of n 5 scores has a mean of M = 12. What is X for this sample? a. 125 = 2.40 b. 512 = 0.417 c. 5(12) = 60 d. Cannot be determined from the information givenA sample has a mean of M = 72. If one person with a score of X = 58 is removed from the sample, what effect will it have on the sample mean? a. The sample mean will increase. b. The sample mean will decrease. c. The sample mean will remain the same. d. Cannot be determined from the information given.One sample of n = 4 scores has a mean of M = 10, and a second sample of n 4 scores has a mean of M - 20. If the two samples are combined, then what value will be obtained for the mean of the combined sample? a. Equal to 15 b. Greater than 15 but less than 20 c. Less than 15 but more than 10 d. None of the other choices is correct.4LCA population of N = 10 scores has a mean of 30. If every score in the distribution is multiplied by 3, then what is the value of the new mean? a. Still 30 b. 33 c. 60 d. 90What is the median for the following set of scores? Scores: 1, 5, 7, 19 a. 5 b. 5.5 c. 6 d. 6.52LCFind the precise median for the following scores measuring a continuous variable. Scores: 1, 4, 5. 5, 5, 6, 7, 8 a. 5 b. 5.17 c. 5.67 d. 6For the sample shown in the frequency distribution table, what is the mode? a. 4 b. 3 c. 2.5 d. 2 X f 5 1 4 2 3 3 2 4 1 2If the mean, median, and mode are all computed for a distribution of scores, which of the following statements cannot be true? a. No one had a score equal to the mean. b. No one had a score equal to the median. c. No one had a score equal to the mode. d. All of the other three statements cannot he true.3LCFor a distribution of scores, the mean is equal to the median. What is the most likely shape of this distribution? a. Symmetrical b. Positively skewed c. Negatively skewed d. Impossible to determine the shapeFor a positively skewed distribution with a mode of X = 20 and a median of X = 25, what is the most likely value for the mean? a. Greater than 25 b. Less than 20 c. Between 20 and 25 d. Cannot be determined from the information givenFor a negatively skewed distribution, what is the most probable order for the three measures of central tendency from smallest to largest? a. Mean, median, mode b. Mean, mode, median c. Mode, mean, median d. Mode, median, mean1LCWhat is the best measure of central tendency for an extremely skewed distribution of scores? a. The mean b. The median c. The mode d. Central tendency cannot be determined for a skewed distribution.One item on a questionnaire asks students to identify their preferred costume for the school mascot from three different choices. What is the best measure of central tendency for the data from this question? a. The mean b. The median c. The mode d. Central tendency cannot be determined for these data.A sample of n = 9 scores has X = 108. What is the sample mean?Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6A population of N = 7 scores has a mean of = 13. What is the value of X for this population?One sample of n = 10 scores has a mean of 8 and a second sample of n 5 scores has a mean of 2. If the two samples are combined, what is the mean for the combined sample?One sample has a mean of M 6 anti h second sample has a mean of M 12. 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 = 6? c. What is the mean for the combined set if the first sample has n = 6 and the second sample has n = 3?A sample with a mean of M = 8 has X = 56. How many scores are in the sample?Find the mean for the scores in the following frequency distribution table: X f 6 1 5 4 4 2 3 2 2 1In a sample of n 6 scores, five of the scores are each above the mean by one point. Where is the sixth score located relative to the mean?A population has a mean of 40. a. If 5 points are added to each score, what is the value for the new mean? b. If each score is multiplied by 3, what is the value for the new mean?Solve the following problems. a. After 8 points are added to each score in a sample, the mean is found to be M = 40. What was the value for the original mean? b. After every score in a sample is multiplied by 5, the mean is found to be M = 40. What was the value for the original mean?A sample of n = 8 scores has a mean of M = 7. If one score is changed from X = 20 to X = 4, what is the value of the new sample mean?A sample of n = 5 scores has a mean of M = 12. If one new score with a value of X 18 is added to the sample, then what is the mean for the new sample?A population of N = 10 scores has a mean of = 12. If one score with a value of X 21 is removed from the population, then what is the value of the new population mean?A sample of n 6 scorns has a mean of M = 14. After one new score is added, the new sample has a mean of M = 12. What is the value of the score that was added?A population of N = 7 scores has a mean of = 9. After one score is removed, the new population has a mean of 10. What is the value of the score that was removed?Find the median for the following set of scores: 1, 9, 3, 6, 4, 3, 11, 10Find the median for the distribution of scores in the following frequency distribution table. X f 6 1 5 1 4 4 3 2 2 3 1 1For the following sample of n 10 scores; 2, 3, 4, 4, 5, 5, 5, 6, 6, 7 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.Find the mean, median, and mode for the distribution of stores in the following frequency distribution table. X f 9 1 8 1 7 3 6 4 5 1Find the mean, median, and mode for the following scores; 8, 7, 5, 7, 0, 10, 2, 4, 11, 7, 8, 7Solve the following problems. a. Find the mean, median, and mode for the following scores. b. Based on the three values for central tendency, what is the most likely shape for this distribution of scores (symmetrical, positively skewed, or negatively skewed)?Solve the following problems. a. Find the mean, median, and mode for the scores in the following frequency distribution table. X f 5 2 4 5 3 2 2 3 1 0 0 2 b. Based on the three values for central tendency, what is the most likely shape for this distribution of scores (symmetrical, positively skewed, or negatively skewed)?Identify the circumstances in which the median may be better than the mean as a measure of central tendency and explain why.Which of the following is a consequence of increasing variability? a. The distance from one score to another tends to increase and a single score tends to provide a more accurate representation of the entire distribution. b. The distance from one score to another tends to increase and a single scone tends to provide a less accurate representation of the entire distribution. c. The distance from one score to another tends to decrease and a single score tends to provide a more accurate representation of the entire distribution. d. The distance from one score to another tends to decrease and a single score tends to provide a less accurate representation of the entire distribution.What is the range for the following set of scores? Scores: 5, 7, 9, 15 a. 4 points b. 5 points c. 10 or 11 points d. 15 pointsFor the following scores, which of the following actions will increase the range? Scores: 3, 7, 10, 15 a. Add 4 points to the score X = 3 b. Add 4 points to the score X 7 c. Add 4 points to the score X = 10 d. Add 4 points to the score X = 15.Which of the following sets of scores has the largest variance? a. 1, 3, 8, 12 b. 12, 13, 14, 15 c. 2, 2, 2, 2 d. 22, 24, 25, 27What is the variance for the following set of scores? Scores: 4, 1, 7 a. = 22. b. 18 c. 9 d. 6A set of scores ranges from a high of X = 24 to a low of X = 12 and has a mean of 18. Which of the following is the most likely value for the standard deviation for these scores? a. 3 points b. 6 points c. 12 points d. 24 pointsWhat is SS, the sum of the squared deviations, for the following population of N = 5 scores? Scores: 1.9,0,2,3 a. 10 b. 41 c. 50 d. 95What is the standard deviation for the following population of scores? Scores: 1.3.9.3 a. 36 b. q c. 6 d. 33LCWhich of the following explains why it is necessary to make a correction to the formula for sample variance? a. a. If sample variance is computed by dividing by n, instead of n 1, the resulting values will tend to underestimate the population variance. b. b. If sample variance is computed by dividing by n, instead of n 1, the resulting values will tend to overestimate the population variance. c. c. If sample variance is computed by dividing by n 1 instead of n, the resulting values will tend to underestimate the population variance. d. d. If sample variance is computed by dividing by n 1 instead of n, the resulting values will tend to underestimate the population variance.Under what circumstances is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a sample? a. When the sample mean is a whole number b. When the sample mean is not a. whole number c. When the sample variance is a whole number d. When the sample variance is not a whole number3LCA researcher takes a sample from a population and computes a statistic for the sample. Which of the following statements is correct? a. If the sample statistic overestimates the corresponding population parameter, then the statistic is biased. b. If the sample statistic underestimates the corresponding population parameter, then the statistic is biased. c. If the sample statistic is equal to the corresponding population parameter, then the statistic is unbiased. d. None of the aboveA researcher takes all of the possible samples of n 4 from a population. Next, the researcher computes a statistic for each sample and calculates the average of all the statistics. Which of the following statements is the most accurate? a. If the average statistic overestimates the corresponding population parameter, then the statistic is biased. b. If the average statistic underestimates the corresponding population parameter, then the statistic is biased. c. If the average statistic is equal to the corresponding population parameter, then the statistic is unbiased. d. All of the above.All the possible samples of n = 3 scores are selected from a population with n - 30 and a - 5 and the mean is computed for each of the samples. If the average is calculated for all of the sample means, what value will be obtained? a. 30 b. Greater than 30 c. Less than 30 d. Near 30 but not exactly equal to 30.If a normal-shaped population with y. 40 and o 5 is shown in a frequency distribution graph, how would the mean and standard deviation be represented? a. The mean is represented by a vertical line drawn at X = 40 and the standard deviation is represented by a vertical line drawn at X 45. b. The mean is represented by an arrow under the graph panting up X = 40 and the standard deviation is represented by a vertical line drawn at X 45 c. The mean is represented by a vertical line drawn at X - 40 and the standard deviation is represented by a horizontal line drawn from X = 40 to X = 45. d. The mean is represented by an arrow under the graph pointing up X 40 and the standard deviation is represented by a horizontal line drawn from X 40 to X - 45If 5 points are added to every score in a population with a mean of = 45 and a standard deviation of = 6, What are the new values for and ? a. = 45 and it = 6 b. = 45 and = 11 c. = 50 and = 6 d. = 50 and = 11A research study obtains a mean of 12.7 and a standard deviation of 2.3 for a sample of n = 25 participants. How would the sample mean and standard deviation be reported in a research journal report? a. M = 12.7 and s = 2.3 b. M = 17.7 and SD = 23 c. Mn= 12.7 and s = 2.3 d. Mn =12.7 and SD = .3For which of the following distributions would X = 35 be an extreme score? a. = 30 and =5 b. = 30 and = 10 c. = 25 and = 5 d. . - 25 and 10Briefly explain the goal for defining and measuring variability.What is the range for the following set of scores? (You may have more than one answer.) Scores: 6, 12, 9, 17, 11, 4, 14In words, explain what is measured by variance and standard deviation.Is it possible to obtain a negative value for variance or standard deviation?Describe the scores in a sample that has a standard deviation of zero.There are two different formulas or methods that can be used to calculate SS. a. Under what circumstances is the definitional formula easy to use? b. Under what circumstances is the computational formula preferred?Calculate the mean and SS (sum of squared deviations) for each of the following sets of scores. Based on the value for the mean, you should be able to decide which SS formula is better to use. Set A: 2, 6, 3, 1 Set B: 2, 4, 1, 3For the following population of N = 9 scores: 4, 2, 0, 5, 3, 2, 1, 7, 3 a. Sketch a histogram showing the population distribution. b. Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.2). c. Compute SS, variance, and standard deviation for the population. (How well does your estimate compare with the actual value of ?)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 standard deviation for the following population of N = 8 scores: 1, 3, 1, 10, 1, 0, 1, 3. (Note: The computational formula works well with these scores.)Calculate SS. variance, and standard deviation for the following population of N = 7 scores: 8, 1, 4, 3, 5, 3, 4. (Note: The definitional formula works well with these scores)For the following set of scores; 6, 2, 3, 0, 4 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?'Explain why the formula for sample variance is different from the formula for population variance.For the following sample or n = 6 scores: 0, 11, 5, 10, 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 sample. (How well does your estimate compare with the actual value of s?)Calculate SS, variance, and standard deviation for the following sample of n = 8 scores: 0, 4, 1, 3, 2, 1, 1, 0.Calculate SS, variance, and standard deviation for the following sample of n = 5 scores: 2, 9, 5, 5, 9.A population has a mean of = 50 and a standard deviation of = 10. a. If 3 points were added to every score in the population, what would be the new values for the mean and standard deviation? b. If every score in the population were multiplied by 2, then what would be the new values for the mean and standard deviation?Solve the following problems. a. After 6 points have been added to every score in a sample, the mean is found to be M = 70 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 s = 18. What were the values for the mean and standard deviation for the original sample?Compute the mean and standard deviation for the following sample of n = 5 scores: 70, 72, 71, 80, and 77. Hint: To simplify the arithmetic, you can subtract 70 points from each score to obtain a new sample. Then, compute the mean and standard deviation for the new sample. Finally, make the correction for having added 70 points to each score to find the mean and standard deviation for the original sample.For the following sample of n = 8 scores: 0, 1,12, 0, 3, 12, 0, 1 a. Simplify the arithmetic by first multiplying each score by 2 to obtain a new sample. Then, compute the mean and standard deviation for the new sample. b. Starting with the values you obtained in part a, make the correction for having multiplied by 2 to obtain the values for the mean and standard deviation for the original sample.For the following population of N = 6 scores: 2, 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 influences 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. a. Compute the range (choose either definition), the variance, and the standard deviation for the following sample of n = 4 scores. Note that there are two scores located in the center of the distribution and two extreme values. Scores: 0, 6, 6, 12 b. Now we will increase the variability by moving the two central scores out to the extremes. Once again compute the range, the variance, and the standard deviation. New scores: 0, 0, 12, 12 c. According to the range, how do the two distributions compare in variability? How do they compare according to the variance and standard deviation?For the data in the following sample: 1, 1, 9, 1 a. Find the SS, variance, and standard deviation. b. Now change the score of X = 9 in X = 3, and find the new values for SS, variance, and standard deviation. c. Describe how one extreme score influences the mean and standard deviation.Arden and Plomin (2006) published a study reporting that IQ scores for boys are more variable than IQ scores for girls. A researcher would like to know if this same phenomenon applies to other measures of cognitive ability. A standard cognitive skills test is given to a sample of n = 15 adolescent boys and a sample of n = 15 adolescent girls, and resulted in the following scores. a. a Compute the mean, the variance, and the standard deviation for each group. b. Is one group of scores noticeably more variable than the other?A population has a mean of = 50 and a standard deviation of = 20. a. Would a score of X 70 be considered an extreme value (out in the tail) in this sample? b. 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 = 39, you obtain a score of X = 35. a. Would you prefer a standard deviation of s = 2 or s = 8? (Hint: Sketch each distribution and find the location of your score.) b. If your score were X = 43, would you prefer s = 2 or s = 8? Explain your answer.What location in a distribution corresponds to z = -2.00? a. Above the mean by 2 points b. Above the mean by a distance equal to 2 standard deviations c. Below the mean by 2 points d. Below the mean by a distance equal to 2 standard deviationsFor a population with = 80 and = 12, what is the z-score corresponding to X = 92? a. +0.50 b. + 1.00 c. + 1.20 d. + 12.00For a sample with M 72and s 4, what is the X value corresponding to z = 2.00? a. X = 70 b. X = 68 c. X = 64 d. X = 60In a population with = 60. a score of X = 58 corresponds to a z-score of z 0.50. What is the population standard deviation? a. 1 b. 2 c. 4 d. Cannot he determined without additional informationIn a sample with a standard deviation of s = 8, a score of X = 64 corresponds to z = - 0.50. What is the sample mean? a. M = 56 b. M = 60 c. M = 68 d. M = 123LC4LC1LCA sample with a mean of M = 50 and a standard deviation of s = 12 is being transformed into z-scores. After the transformation, what is the standard deviation for the sample of z-scores? a. n b. 1 c. n 1 d. nWhich of the following is an advantage of transforming X values into z-scores? a. All negative numbers are eliminated. b. The distribution is transformed to a normal shape. c. All scores are moved closer to the mean. d. None of the other options is an advantage.Last week Sarah had exams in math and in Spanish. On the math exam, the mean was = 30 with = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was = 60 with = 6 and Sarah had a score of X = 65. For which class should Sara expect the better grade? a. Math b. Spanish c. The grades should be the same because the two exam scores are in the same location. d. There is not enough information to determine which is the better grade.A set of scores has a mean of = 63 and a standard deviation of = 8. If these scores are standardized so that the new distribution has = 50 and = 10, what new value would be obtained for a score of X = 59 from the original distribution? a. The score would still be X = 59. b. 45 c. 46 d. 55A distribution with = 35 and = 8 is being standardized so that the new mean and standard deviation will be = 50 and = 10. When the distribution is standardized, what value will be obtained for a score of X = 39 from the original distribution? a. X = 54 b. X = 55 c. X = 1.10 d. Impossible to determine without more informationUsing z-scores, a sample with M = 37 and s = 6 is standardized so that the new mean is M = 50 and s = 10. How does an individuals z-score in the new distribution compare with his/her z-Score in the original sample? a. New z = old z + 13 b. New z =(10/6)(old z) c. New z = old z d. Cannot be determined with the information givenFor the past 20 years, the high temperature on April 15th has averaged = 62 degrees with a standard deviation of - 4. Last year, the high temperature was 72 degrees. Based on this information, last years temperature on April 15th was ________ a. A little above average b. Far above averageA Score of X = 73 is obtained from a population. Which set of population parameters would make X = 73 and extreme, unrepresentative score? a. = 65 and = 8 b. = 65 and = 3 c. . = 70and = 8 d. = 70 and = 3Under what circumstances would a score that is 15 points above the mean be considered an extreme score? a. When the mean is much larger than 15 b. When the standard deviation is much larger than 15 c. When the mean is much smaller than 15 d. When the standard deviation is much smaller than 15Explain how a z-score identifies an exact location in a distribution with a single number.For a population with a standard deviation of = 20. find the z-score for each of the following locations in the distribution a. Above the mean by 5 points b. Above the mean by 2 points c. C. Below the mean by 10 points d. Below the mean by 30 pointsFor a sample with a standard deviation of s = 12. describe the location of each of the following z-scores in terms of its position relative to the mean. For example. Z= + 1 00 is a location that is 12 points above the mean. a. z = 2.00 b. z = +0.75 c. z =+1.00 d. z =1.50For a population with = 40 and = 8: a. Find the z-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 =44X = 4HX = 56 X = 38X = 34X = 32 b. 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 = 1.50 z= -0.50z = -1.25z = -2.50For a population with = 80 and = 9. find the z-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 =- 83X = 75X = Q1 X = 67X = R5X = 68A sample has a mean of M = 90 and a standard deviation of s = 20. a. Find the z-score for each of the following X values. X=95X = 98X = 105 X = 80X = 88X = 76 b. Find the X value for each of the following z-scores z= 1.00z 0.50z= 1.50 z = 0.75z= 1.25z = 2.60A sample has a mean of M =60 and a standard deviation of s = 7. For this sample, find the z-score for each of the following X values. X = 69X = 72X = 63 X = 54X = 49X = 52R. Fine the-. z-score corresponding to a |score of Y - 10 for each of the following distributions. a. = 50 and = 20 b. = 50 and = 10 c. = 20 and = 5 d. = 20 and = 2Fine the x value corresponding to z. - 0.75 for of the following distributions. a. = 90 and = 4 b. = 90 and = 8 c. = 90 and = 12 d. = 90 and = 20Find the z-score corresponding to X 40 and the X value corresponding to z = 0.25 for each of the following populations. a. . = 50 and = 20 b. . = 50 and = 4 c. = 30 and = 8 d. = 30 and = 4Find the e-score corresponding to X = 24 and the X value corresponding to z = 1.50 for each of the following samples. a. M =20 and s = 12 b. M =20 and s = 4 c. M =30 and s = 8 d. M =30 and s = 10A score that is 12 points below the mean corresponds to h z-sr.nrr of Z = 1.50. What is the standard deviation?A score that is 20 points above the mean corresponds to a z-score of z 1.25. What is the standard deviation?For a population with a standard deviation of = 14, a score of X 24 corresponds to z 0.50. What is the population mean?For a population with a mean of = 45, a score of X 54 corresponds to z 1.50. What is the population standard deviation?For a sample with a standard deviation of s 6, a score of X 30 corresponds to z. = 1.50 What is the sample mean?For a sample with a mean of M - 63, a score of X = 54 corresponds to z = 0.75. What is the sample standard deviation?In a population distribution, a score of X = 57 corresponds to z = 0.25 and a score of X = 87 corresponds to z = 1.25, Find the mean and standard deviation for the population, (Hint: Sketch the distribution and locale the two scores on your sketch.)In a sample distribution, a score of V 21 corresponds to z = 1.00 and a score of X = 12 corresponds to z = 2.50. Find the mean and standard deviation for the samples.A distribution of exam scores has a mean of = 42. a. If your score is X = 46, which standard deviation would give you a better grade: 5 or 10? b. If your score is X = 38, which standard deviation would give you a belter grade: = 5 or = 10?For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer. a. A score of X 70, on an exam with M 82 and = 8; or a score of X =60 on an exam with = 72 and = 12. b. A score of X 58, on an exam with 49 and = 6; or a score of X =85 on an exam with = 70 and = 10. c. A score of X 32, on an exam with 24 and = 4; or a score of X =26 on an exam with = 20 and = 2.A population with a mean of = 41 and a standard deviation of = 4 is transformed into a standardized distribution with 100 and 20. Find the new. standardized score for each of the following values from the original population. a. X = 39 b. X = 36 c. X = 45 d. X = 50A sample with a mean of M = 62 and a standard deviation of s = 5 is transformed into a standardized distribution with = 50 and = 10. Find the new. Standardized score for each of the following values from the original population. a. X = 61 b. X = 55 c. X = 65 d. X = 74A population consists of the following N 6 scores: 2, 4, 1, 2, 7, 2 a. Compute and for the population. b. Find the z-score for each score in the population. c. Transform the original population into a new population of N = 5 scores with a mean of = 50 and a standard deviation of = 10.A sample consists of the Following n = 5 scores: 8, 4, 10, 0.3. 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 100 and s 20For 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) or an extreme score (far out in the tail of the distribution)? a. = 75 and = 15 b. = 80 and = 2 c. = 90 and = 20 d. = 93 and = 3An introductory psychology class with n = 44 students has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. If one student is randomly selected from this class, what is the probability of getting a sophomore? a. 8/24 b. 20/24 c. 20/44 d. 14/44A jar contains 10 red marbles and 20 blue marbles. If one marble is selected from this jar, what is the probability that the marble will be red? a. 1/30 b. 1/30 c. 10/30 d. 10/30Random sampling requires sampling with replacement. What is the goal of sampling with replacement? a. It ensures that every individual has an equal chance of selection. b. It ensures that the probabilities stay constant from one selection to the next. c. It ensures that the same individual is nor selected twice d. All of the other options are goals of sampling with replacement.What is the probability of randomly selecting a z-score less than z = 0.25 from a normal distribution? a. 0.5987 b. 0.4013 c. - 0.5987 d. 0.4013In a normal distribution, what z-score value separates the highest 90% of the scores from the rest of the distribution? a. z - 1.28 b. z = - 1.28 c. z. = 0.13 d. z = - 0.13In a normal distribution, what z-score value separates the lowest 20% of the distribution from the highest 80%? a. z = 0.20 b. z = 0.80 c. z = 0.84 d. z = - 0.84The population of SAT scores forms a normal distribution with a mean of . 500 and 100. What proportion of the population consists of individuals with SAT scores lower than 400? a. 0.1587 b. 0.8413 c. 0.34.13 d. - 0.15.87A normal distribution has = 100 and = 20. What is the probability of randomly selecting a score of less than 130 from this distribution? a. p - 0.9032 b. p 0.9332 c. p - 0.0968 d. p- 0.0668For a normal distribution with = 70 and a 10, what is the minimum score necessary to be in the top 60% of the distribution? a. 67.5 b. 62.5 c. 65.2 d. 68.4Which of the following accurately describes a score of X - 52 or larger in a normal distribution with , = 40 and = 5? a. It is an extreme, very unlikely score. b. It is higher than average but not extreme or unlikely. c. It is a little above average. d. It is an average, representative score.For a normal distribution with = 60 and = 10, what X values form the boundaries between the middle 95% of the distribution and the extreme 5% in the tails? a. 51.6 and 68.4 b. 47 7 and 72.8 c. 43.5 and 65.5 d. 40 4 and 79 63LCWhat 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 containing a mixture or 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? a. Randomly selecting a Milky Way bar b. Randomly selecting either a Snickers or a Twix bar c. Randomly selecting something other than a Twix barA psychology class consists of 28 males and 52 females. If the professor selects names from the class list using random sampling. a. what is the probability that the first student selected will be a female? b. and if a random sample of n = 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male?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 = 2.00 b. z =0.75 c. z = 1.40 d. z = 0.67Draw 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 = 0.40Draw a vertical line through a normal distribution for each of the following z-score locations. Find the proportion of the distribution located between the mean and the z-score. a. z = 1.80 b. z = 0.55 c. z = 1.10 d. z = 0.85Find each of the following probabilities for a normal distribution. a. p(z 2.25) b. p(z 1.20) c. p(z 0.40) d. p(z 1.75)What proportion of a normal distribution is located between each of the following z = score boundaries? a. z = 0.50 and z = +0.50 b. z = 0.85 and z = +0.85 c. z = 1.60 and z = +1.60Find each of the following probabilities for a normal distribution. a. p(-1.80 z 0.20) b. p(-1.80 z 0.20) c. p(0.25 z 1.25) d. (-0.90 z - 0.60)Find the z-score location of a vertical line that separates a normal distribution as described in each of the following. a. 15% in the tail on the right b. 40% in the tail on the. left c. 75% in the body on the right d. 60% in the body on the leftFind the z-score boundaries that separate a normal distribution as described in each of the following, a. The middle 20% from the 80% in the tails b. The middle 25% from the 75% in the tails c. The middle 70% from the 30% in the tails d. The middle 90% from the 10% in the tailsA normal distribution has a mean of . = 90 and a standard deviation of = 15 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 a. X = 93 b. X = 110 c. X = 85 d. X = 70A normal distribution but a name of = 60 and a standard deviation of = 16 For each of the following scores, indicate whether the body is to the right or left of the score and find the proportion of the distribution located in the body. a. X = 64 b. X = 80 c. X = 52 d. X = 28For a normal distribution with a mean of = 85 and standard deviation of = 20 find the proportion of the population corresponding to each of the following. a. Scores greater than 89 b. Scores less than 72 c. Scores between 70 and 100In 2014 the New York Yankee had a team batting average of 245 (actually 0.245 but we will avoid the decimals). Of course, the balling avenge varies from game to game, but assuming that the distribution of batting averages for 162 games is normal with a standard deviation of = 40 points, answer each of the following. a. If you randomly select one game from 2014, what is the probability that the team balling average was over 300? b. If you randomly select one game from 2014, what is the probability that the team batting average was under 200?IQ test scores are standardized to produce a normal distribution with a mean of - 100 and a standard deviation of -15. Find the proportion of the population in each of the following IQ categories. a. Genius or near genius. IQ over 140 b. Very superior intelligence: IQ from 120 to 140 c. Average or normal intelligence: IQ from 90 to 109The distribution of scores on the SAT it approximately normal with a mean of 500 and a standardAccording to a recent report, the average American consumes 22.7 teaspoons of sugar each day (National Geographic Magazine, August 2013). Assuming that the distribution is approximately normal with a standard deviation of = 4.5, find each of the following values. a. What proportion of people consume more than 30 teaspoon of sugar a day? b. What proportion of people consume at least 20 teaspoon of sugar a day?A recent report indicates that 2-year-old children from well-educated suburban families watched an average of = 60 minutes of television each day. Assuming that the distribution of television-watching times is normal with a standard deviation of = 25 minutes, find each of the following proportions. a. What proportion of 2-year-old children watch more than 2 hours of television each day? b. What proportion of 2-year-old children watch less than 30 minutes a day?A report in 2010 indicates that Americans between the ages of 8 and 18 spend an average of = 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 = 2.5 hours and find the following values. a. What is the probability of selecting an individual who uses electronic devices more than 9 hours a day? b. What proportion of 8-to 18-year-old Americans spend between 8 and 12 hours per day using electronic devices? In symbols, p(8 X 12) = ?Seattle, Washington, averages = 34 inches of annual precipitation. Assuming that the distribution of precipitation amounts is approximately normal with a standard deviation of = 6.5 inches, determine whether each of the following represents a fairly typical year, an extremely wet year, or an extremely dry year. a. Annual precipitation of 41.8 inches b. Annual precipitation of 49.6 inches c. Annual precipitation of 28.0 inchesIf all the possible random samples, each with n = 9 scores, are selected from a normal population with = 80 and = 18, and the mean is calculated for each sample, then what is the average value for all of the sample means? a. 9 b. 80 c. 9(80) = 720 d. Cannot be determined without additional informationAll the possible random samples of size n = 2 are selected from a population with = 40 and = 10 and the mean is computed for each sample. Then all the possible samples of size n = 25 are selected from the same population and the mean is computed for each sample. How will the distribution of sample means for n = 2 compare with the distribution for n = 25? a. The two distributions will have the same mean and variance. b. The mean and the variance for n = 25 will both be larger than the mean and variance for n = 2. c. The mean and the variance for n = 25 will both be smaller than the mean and variance for n = 2. d. The variance for n = 25 will be smaller than the variance for n = 2 but the two distributions will have the same mean.If all the possible random samples of size n = 25 are selected from a population with = 80 and = 10 and the mean is computed for each sample, then what shape is expected for the distribution of sample means? a. The sample means tend to form a normal-shaped distribution. b. The distribution of sample means will have the same shape as the sample distribution. c. The sample will be distributed evenly across the scale, forming a rectangular-shaped distribution. d. There are thousands of possible samples and it is impossible to predict the shape of the distribution.If random samples, each with n = 4 scores, are selected from a normal population with = 80 and = 10, then what is the expected value of the mean for the distribution of samplemeans? a. 2.5 b. 5 c. 40 d. 80If random samples each with n = 9 scores, are selected from a normal population with = 80 and = 18, and the mean is calculated for each sample, then how much distance is expected on average between M and .? a. 2 points b. 6 points c. 18 points d. Cannot be determined without additional informationA sample of n = 4 scores has a standard error of 12. What is the standard deviation of the population from which the sample was obtained? a. 48 b. 24 c. 6 d. 3A sample of n = 16 scores is obtained from a population with = 70 and = 20. If the sample mean is M = 75, then what is the z-score corresponding to the sample mean? a. z = 0.25 b. z = 0.50 c. z = 1.00 d. z = 2.00A random sample of n = 4 scores is obtained from a normal population with = 20 and = 4. What is the probability of obtaining a mean greater than M = 22 for this sample? a. 0.50 b. 1.00 c. 0.1587 d. 0.3085A random sample of n = 4 scores is obtained from a normal population with = 40 and = 6. What is the probability of obtaining a mean greater than M = 46 for this sample? a. 0.3085 b. 0.1587 c. 0.0668 d. 0.0228Which of the following would cause the standard error of M to get smaller? a. Increasing both the sample size and standard deviation b. Decreasing both the sample size and standard deviation c. Increasing the sample size and decreasing the standard deviation d. Decreasing the sample size and increasing the standard deviationA sample obtained from a population with = 10 has a standard error of 2 points. How many scores are in the sample? a. n = 5 b. n = 10 c. n = 20 d. n = 253LCA sample is obtained from a population with = 100 and = 20. Which of the following samples would produce the z-score closest to zero? a. A sample of n = 25 scores with M = 102 b. A sample of n = 100 scores with M = 102 c. A sample of n = 25 scores with M = 104 d. A sample of n = 100 scores with M = 104For a normal population with = 80 and = 20, which of the following samples is least likely to be obtained? a. M = 88 for a sample of n = 4 b. M = 84 for a sample of n = 4 c. M = 88 for a sample of n = 25 d. M = 84 for a sample of n = 25For a sample selected from a normal population with = 100 and = 15, which of the following would be the most extreme and unrepresentative? a. M = 90 for a sample of n = 9 scores b. M = 90 for a sample of n = 25 scores c. M = 95 for a sample of n = 9 scores d. M = 95 for a sample of n = 25 scoresBriefly define each of the following: a. Distribution of sample means b. Central limit theorem c. Expected value of M d. Standard error of MA sample is selected from a population with a mean of = 65 and a standard deviation of = 15. a. If the sample has n = 9 scores, what is the expected value of M and the Standard error of M? b. If the sample has n = 25 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.Under what circumstances is the distribution of sample means definitely a normal distribution?A random sample is selected from a population with a standard deviation of = 18. a. On avenge, 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? b. On average, how much difference should there be for a sample of n = 9 scores? c. On average, how much difference should there be for a sample of n - 36 scores?For a sample of n = 16 scores, what is the value of the population standard deviation () necessary to produce each of the following standard error values? M = 8 points M = 4 points M = l pointFor a population with a mean of = 40 and a standard deviation of = 8, find the z-score corresponding to each of the following samples. a. X = 34 for a sample of n = 1 score b. M = 34 for a sample of n = 4 scores c. M = 34 for a sample of n = 16 scoresA sample of n - 25 scores has a mean of M - 68 Find the z-score for this sample: a. If it was obtained from a population with = 60 and = 10 b. If it was obtained from a population with = 60 and = 20 c. If it was obtained from a population with = 60 and = 40A population forms a normal distribution with a mean of = 85 and a standard deviation of = 24. For each of the following samples, compute the z-score for the sample mean. a. M = 91 for n = 4 scores b. M = 91 for n = 9 scores c. M = 91 for n = 16 scores d. M = 91 for n = 36 scoresScores on a standardized reading test for fourth-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. A sample of n = 16 Students b. A sample of n = 25 Students c. A sample of n = 100 StudentsScores from a questionnaire measuring social anxiety form a normal distribution with a mean of = 50 and a standard deviation of = 10. What is the probability of obtaining a sample mean greater than M = 53. a. for a random sample of n = 4 people? b. for a random sample of n = 16 people? c. for a random sample of n = 25 people?A normal distribution has a mean of = 54 and standard deviation of = 6. What is the probability of randomly selecting a score less then X = 51? What is the probability of selecting a sample of n = 4 scores with a mean less than M = 51? c. 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 = 8 a. 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? b. 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? c. 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? d. 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 = 16 selected from a normal distribution with a mean of = 75 and a standard distribution of - 20. find each of the following: a. The range of sample means that defines the middle 95% of the distribution of sample means b. The range of sample means that defines the middle 99% of the distribution of sample meansThe distribution exam grades for an introductory psychology class is negatively skewed with a mean of . 71.5 and a standard deviation of = 12. a. What is the probability of selecting a random sample of n = 9 students with an average grade greater than 75? (Careful: This is a trick question.) b. What is the probability of selecting a random sample of n = 36 students with an average grade greater than 75? c. For a sample of n - 36 students, what is me probability that the average grade is between 70 and 75?By definition, jumbo shrimp are those that require between 10 and 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag average = 12.5 with a standard deviation of - 1.5, and forms a normal distribution. What is the probability of randomly picking u sample of n = 25 1-pound bags that average more than M = 13 shrimp per bag?For a population with a mean of = 72 and a standard deviation of = 10, what is the standard error of the distribution of sample means for each of the following sample sizes? a. n = 4 scores b. n = 25 scoresFor a population with = 16, how large a sample is necessary to have a standard error that is a. less than 8 paints? b. less than 4 points? c. less than 2 points?If the population standard deviation is = 10, how large a sample is necessary to have a standard error that is a. less than 5 points? b. less than 2 points? c. less than 1 point?Junes, Thomas, and Piper (2003) conducted a study to evaluate the effect of alcohol on judgments of attractiveness for members of the opposite sex. Male college students who had cither no alcohol or moderate alcohol consumption were shown photographs of females and asked to judge the attractiveness of each face on a 7-point scale (7 = highest). Data similar to the results obtained in the study are shown in the following table. Alcohol Consumption Mean SE None 3.4 0.20 Moderate 4.09 0.22 a. Construct a bar graph that incorporates all of the information in the table. b. Looking at your graph, do you think that alcohol con sumption has an effect on perceived attractiveness?A normal distribution has a mean of = 60 and a standard deviation of = 12. 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. a. M = 64 for n = 4 scores b. M = 64 for n = 9 scores c. M = 66 for n = 16 scores d. M = 66 for n = 36 scoresA random sample is obtained from a normal population with a mean of - 76 and a standard deviation of = 20. The sample mean is = 84. a. Is this a representative sample mean or an extreme value for a sample of n = 4 scores? b. Is this a representative sample mean or an extreme value for a sample of n = 25 Scores.A sample of n= 36 scores is selected from a normal distribution with a mean of = 65. If the sample mean is M =59, then compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for each of the following: a. A population standard deviation of = 12 b. A population standard deviation of = 30In general terms, what is a hypothesis test? 1. A descriptive technique that allows researchers to describe a sample 2. A descriptive technique that allows researchers to describe a population 3. An inferential technique that uses the data from a sample to draw inferences about a population 4. An inferential technique that uses information about a population to make predictions about a sampleA sample is selected from a population with a mean of = 60 and a treatment is administered to the individuals in the sample. If a hypothesis test is used to evaluate the treatment effect, then what is the correct statement of the null hypothesis? a. = 60 b. 60 c. M = 60 d. M 60Which of the following accurately describes the critical region for a hypothesis test? a. Outcomes that have a very low probability if the null hypothesis is true b. Outcomes that have a high probability it the null hypothesis is true c. Outcomes that have a very low probability whether or not the null hypothesis is true d. Outcomes that have a high probability whether or not the null hypothesis is trueA sample of n - 25 individuals is selected from a population with = 80 and a treatment is administered to the sample. Which of the following is the most likely outcome if the treatment has a large effect? a. The sample mean should be very different from 80 and should lead you to reject the null hypothesis. b. The sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis. c. The sample mean should be close to 80 and should lead you to reject the null hypothesis. d. The sample mean should be close to 80 and should lead you to fail to reject the null hypothesis.What does a type II error mean? a. A researcher has falsely concluded that a treatment has an effect. b. A researcher has correctly concluded that a treatment has no effect. c. A researcher has falsely concluded that a treatment has no effect. d. A researcher has correctly concluded that a treatment has an effect.Which of the following defines a Type I error? a. Rejecting a false null hypothesis b. Rejecting a true null hypothesis c. Failing to reject a false null hypothesis d. Failing to reject a true null hypothesis3LCA research report includes the statement, z - 2.18. p .05. What happened in the hypothesis test? a. The obtained sample mean was very unlikely if the null hypothesis is true, so H0 was rejected. b. The obtained sample mean was very likely if the null hypothesis is true, so H0 was rejected. c. The obtained sample mean was very unlikely if the null hypothesis is true, and the test failed to reject H0. d. The obtained sample mean was very likely if the null hypothesis is true, and the test failed to reject H0.2LCWhat assumption is needed before you can use the unit normal table to find critical values for a z-score hypothesis lest? a. The population of scores before treatment is normal. b. The scores are obtained by random sampling. c. c The scores in the sample are independent observation. d. The distribution of sample means is normal.A population is known to have a mean of = 50. A treatment is expected to increase scores for individuals in this population. If the treatment is evaluated using a one-tailed hypothesis, then which of the following is the correct statement of the null hypothesis? a. 50 b. 50 c. 50 d. 50A researcher is conducting an experiment to evaluate a treatment that is expected to decrease the scores for individuals in a population which is known to have a mean of - 80. The results will be examined using a one-tailed hypothesis test. Which of the following is the correct statement of the alternative hypothesis (H1)? a. 80 b. 80 c. 80 d. 80A researcher expects a treatment to produce an increase in the population mean. Assuming a normal distribution, what is the critical z-score for a one-tailed test with = .01? a. + 2.33 b. 2.58 c. + 1.65 d. 2.33Under what circumstances can a very small treatment effect be statistically significant? a. With a large sample and a large standard deviation b. With a large sample and a small standard deviation c. With a small sample and a large standard deviation d. With a small sample and a small standard deviationA sample of n - 9 scores is selected from a population with a mean of = 80 and = 12, and a treatment is administered to the sample. After the treatment, the researcher measures effect size with Cohens d and obtains d 0.25. What was the sample mean? a. M = 81 b. M = 82 c. M = 83 d. M = 84If other factors are held constant, then how does sample size affect the likelihood of rejecting the null hypothesis and the value for Cohens d? a. A larger sample increases the likelihood of rejecting the null hypothesis and increases the value of Cohens d. b. A larger sample increases the likelihood of rejecting the null hypothesis but decreases the value of Cohens d c. A larger sample increases the likelihood of rejecting the null hypothesis but has no effect on the value of Cohens d. d. A larger sample decreases the likelihood of rejecting the null hypothesis but has no effort on the value of Cohens d.If the power of a hypothesis test is found to be p = 0.80, then what is the probability of a Type II error for the same test? a. p = 0.20 b. p = 0.80 c. The probability of a Type II error is not related to power. d. it is impossible to determine without knowing the alpha level for the test.How does the sample size influence the likelihood of rejecting the null hypothesis and the power of the hypothesis test? a. Increasing sample size increases both the likelihood of rejecting H0 and the power of the test. b. Increasing sample size decreases both the likelihood of rejecting H0 and the power of the test. c. Increasing sample size increases the likelihood of rejecting H0 but the power of the test is unchanged. d. Increasing sample size decreases the likelihood of rejecting H0 but the power of the test is unchanged.How is the power of a hypothesis test related to sample size and the alpha level? a. A larger sample and a larger alpha level will both increase power. b. A larger sample and a larger alpha level will both decrease power. c. A larger sample will increase power but a larger alpha will decrease power. d. A larger sample will decrease power but a larger alpha will increase power.Identify the four steps of a hypothesis test as presented in this chapter.Define the alpha level and the critical region for hypothesis test.Define a Type I error and a Type II error and explain the consequences of each.If the alpha level is changed from = .05 to = .01. a. what happens to the boundaries for the critical region? b. what happens to the probability of a Type I error?Explain how each of the following influences the value of the z-score in a hypothesis test. 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 sampleAckerman and Goldsmith (2011) report that students who study from a screen (phone, tablet, or computer) tended to have lower quiz scores than students who studied the same material from primed pages. To test this finding, a professor identifies a sample of n 16 students who used the electronic version of the course textbook and determine that this sample had an average score of M = 72.5 on the final exam. During the previous three years, the final exam scores for the general population of students taking the course averaged = 77 with a standard deviation of = 8 and formed a roughly normal distribution. The professor would like to use the sample to determine whether students studying from an electronic screen had exam scores that are significantly different from those for the general population. a. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variables being examined. b. Using the standard four-step procedure, conduct a two-tailed hypothesis test with = .05 to evaluate the effect of studying from an electronic screen.Babcock and Marks (2010) review survey data from 2003-2005, and obtained an average of 14 hours per week spent studying by full-time students at four-year colleges in the United States. To determine whether this average has changed in recent years, a researcher selected a sample of n 64 of todays 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 selfesteem for adolescents (McGee, Williams, Howden-Chapman, Martin, Karachi, 2006). In a representative study, a sample of n 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of 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-eastern scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with .05. b. Compute Cohens 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 = 40 and a standard deviation of = 6. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 37 a. If the sample consists of n _ 36 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 = 9 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 lest.A random sample of n = 16 stores is selected from a normal population with a mean of = 50. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 54. a. If the population standard deviation is 8, 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 12, 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.In a study examining the effect of humor on interpersonal attractions, McGee and Shevlin (2009) found that a mans sense of humor had a significant effect on how he was perceived by women. In the study, female college students were given brief descriptions of a potential romantic partner and then rated the attractiveness of the male on a scale from 1 (low) to 7 (high). The fictitious male was described positively as being single, ambitious, and having good job prospects. In one condition, the description also said that he had a great sense of humor. The results showed that the description was rated significantly higher when a sense of humor was included. To further examine this effect, a researcher selected a sample of n = 16 college males and asked them to read a brief description of a female and then rate the attractiveness of the woman in the description. The description had been used in previous research but was modified by adding a statement describing a good sense of humor. Based on the previous research, the rating scores for the original description were known to form a normal distribution with = 4.0 with a Standard deviation of 0.60. The sample mean for the modified description was M = 4.42. Do the sample data indicate that adding a sense of humor to the description significantly increases the rating scores? Use a one-tailed test with .05.A random sample is selected from a normal population with a mean of 40 and a standard deviation of 10. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 46. 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 43, what sample size is needed to be significant for a two-tailed test with = .05?Researchers at a National Weather Center in the northeastern United States recorded the number of 90 Fahrenheit 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 90 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 90 days than would be expected for a random sample from this population? Use a one-tailed test with =.05.
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