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All Textbook Solutions for Behavioral Sciences STAT (with CourseMate Printed Access Card) (New, Engaging Titles from 4LTR Press)
What is the goal of behavioral research?Why is it important for students of behavioral research to understand statistics?(a) What is a population? (b) What is a sample? (c)How are samples used to make conclusions about populations? (d) What are researchers really referring to when they talk about the population?(a) What is a variable? (b) What is a quantitative variable? (c) What is a qualitative variable?What pattern among the X and Y scores do you see when: (a) A relationship exists between them? (b) No relationship is present?What is the difference in the pattern among the X and Y scores between (a) a perfectly consistent relationship and (b) a less consistent (weaker) relationship?7SP8SP9SPIn an experiment, what is the dependent variable?What is the difference between the independent variable and the conditions of the independent variable?(a) What are descriptive statistics used for? (b)What are inferential statistics used for?13SP14SP15SPWhat are the two aspects of a study to consider when selecting the descriptive or inferential statistics you should employ?Researcher A gives participants various amounts of alcohol and then observes any decrease in their ability to walk. Researcher B notes the various amounts of alcohol that participants drink at a party and then observes any decrease in their ability to walk. Which study is an experiment, and which is a correlational study? Why?Maria asked a sample of college students about their favorite beverage. Based on what the majority said, she concluded that most college students prefer drinking carrot juice to other beverages! What statistical argument can you give for not accepting this conclusion?In the following experiments, identify the independent variable, the conditions, and the dependent variable: (a) studying whether final exam scores are influenced by whether concurrent background music is soft, loud, or absent; (b) comparing students from small, medium, and large colleges with respect to how much fun they have during the semester; (c) studying whether being first-, second-, or third-born is related to intelligence; (d) studying whether length of daily exposure to a sunlamp (15 versus 60 minutes) accounts for differences in depression; (e) studying whether being in a room with blue walls, green walls, or red walls influences aggressive behavior in adolescents.Use the words relationship, sample, population, statistic, and parameter to describe the flow of a research study to determine whether a relationship exists in nature.21SPWhich sample in problem 21 shows the most consistent relationship? How do you know?What pattern do we see when the results of an experiment show a relationship?Indicate whether a researcher would conduct an experiment or a correlational study when studying: (a) whether different amounts of caffeine consumed in 1 hour influence speed of completing a complex task; (b) the relationship between number of extracurricular activities and GPA; (c)the relationship between the number of pairs of sneakers owned and the persons athleticism; (d) how attractive men rate a woman when she is wearing one of three different types of perfume; (e) the relationship between GPA and the ability to pay off school loans; (f) the influence of different amounts of beer consumed on a persons mood.In the chart below, identify the characteristics of each variable.What do these symbols mean? (a) N; (b) f?Why must the sum of all fs in a sample equal N?(a) What is the difference between a bar graph and a histogram? (b) With what kind of data is each used?What is a dot plotted on a graph called?(a) What is the difference between a histogram and a polygon? (b) With what kind of data is each used?(a) What does it mean when a score is in a tail of a normal distribution? (b) What is the difference between scores in the left-hand tail and scores in the right-hand tail?7SP(a) What is the advantage of computing relative frequency instead of simple frequency? (b) What is the advantage of computing percentile instead of cumulative frequency?(a) What is the difference between the polygon for a skewed distribution and the polygon for a normal distribution? (b) What is the difference between the polygon for a bimodal distribution and the polygon for a normal distribution?What is the difference between the graphs for a negatively skewed distribution and a positively skewed distribution?11SPIn reading psychological research, you encounter the following statements. Interpret each one. (a)The IQ scores were approximately normally distributed. (b) A bimodal distribution of physical agility scores was observed. (c) The distribution of the patients memory scores was severely negatively skewed.What type of frequency graph is appropriate when counting the number of: (a) Blondes, brunettes, redheads, or others attending a college? (b)People having each body weight reported in a statewide survey? (c) Children in each grade at an elementary school? and (d) Car owners reporting above-average, average, or below-average problems with their car?The distribution of scores on a statistics test is positively skewed. What does this indicate about the difficulty of the test?15SP(a) On a normal distribution of exam scores, Crystal scored at the 10th percentile, so she claims that she outperformed 90% of her class. Why is she correct or incorrect? (b) Ernestos score is in a tail of the normal curve, so he claims to have one of the highest scores. Why is he correct or incorrect?Interpret each of the following. (a) You scored at the 35th percentile. (b) Your score has a relative frequency of .40. (c) Your score is in the upper tail of the normal curve. (d) Your score is in the left-hand tail of the normal curve. (e) The cumulative frequency of your score is 50. (f) Using the area under the normal curve, your score is at the 60th percentile.Draw a normal curve and identify the approximate location of the following scores. (a) You have the most frequent score. (b) You have a low-frequency score, but it is higher than most. (c) You have one of the lower scores, but it has a relatively high frequency. (d) Your score seldom occurredThe following shows the distribution of final exam scores in a large introductory psychology class. The proportion of the total area under the curve is given for two segments. (a) Order the scores 45, 60, 70, 72, and 85 from most frequent to least frequent. (b) What is the percentile of a score of 60? (c) What proportion of the sample scored below70? (d) What proportion scored between 60 and 70? (e) What proportion scored above 80? (f) What is the percentile of a score of80?The following normal distribution is based on a sample of data. The shaded area represents 13% of the area under the curve. (a) What is the relative frequency of scores between A and B? (b) What is the relative frequency of scores between A and C? (c) What is the relative frequency of scores between B and C?(d) Rank-order A, B, C, and D to reflect the order of scores from the highest to the lowest frequency. (e) Rank-order A, B, C, and D to reflect the order of scores from the highest to the lowest score.Organize the ratio scores below in a table andshow their simple frequency and relative frequency. 49 52 47 52 52 47 49 47 50 51 50 49 50 50 50 535149Draw a simple frequency polygon using the data in problem 21.What type of graph should you create when counting the frequency of: (a) The brands of cell phones owned by students? Why? (b) The different body weights reported in a statewide survey? Why? (c) The people falling into one of eight salary ranges? Why? (d) The number of students who were absent from a class either at the beginning, middle, or end of the semester? Why?An experimenter studies vision in low light by having participants sit in a darkened room for either 5, 15, or 25 minutes and then testing their ability to correctly identify 20 objects. (a) What is the independent variable here? (b) What are the conditions? (c) What is the dependent variable? (d)You would use the scores from which variable to create a frequency distribution?25SP(a) What does a measure of central tendency indicate? (b) What are the three measures of central tendency?2SP3SP4SP5SP(a) Why does the mean accurately summarize a normal distribution? (b) Why does the mean inaccurately summarize a skewed distribution?7SP8SP9SPWhy do we use the mean of a sample to predict anyones score in that sample?11SP(a) In question 11, what is your best estimate of the median? (b) Why?The following distribution shows the locations of five scores. a. Match the deviation scores -7, +1, 0, -2, and +5 with their locations. A = _____ B = _____ C =_____ D = _____ E = _____ b. Arrange the deviation scores to show the highest to lowest raw scores. c. Arrange the deviation scores to show the raw scores having the highest to lowest frequency.(a) You misplaced one of the scores in a sample, but you have the other data below. What score should you guess for the missing score? (b) Why? 15 12 13 14 11 14 13 13 12 11 15A researcher collected the following sets of data. For each, indicate the measure of central tendency she should compute: (a) the following IQ scores: 60, 72, 63, 83, 68, 74, 90, 86, 74, and 80; (b) the following error scores: 10, 15, 18, 15, 14, 13, 42, 15, 12, 14, and 42; (c) the following blood types: A2, A2, O, A1, AB2, A1, O, O, O, and AB1; (d) the following grades: B, D, C, A, B, F, C, B, C, D, and D.On a normal distribution, four participants obtained the following deviation scores: 5, 0, 3, and 1. (a) Which person obtained the lowest raw score? How do you know? (b) Which personsraw score had the lowest frequency? How do you know? (c) Which persons raw score had the highest frequency? How do you know? (d) Which person obtained the highest raw score? How do you know?Kevin claims a deviation of 5 is always better than a deviation of 5. Why is he correct or incorrect?(a) What is the symbol m called and what does it stand for? (b) How do we usually determine its value?19SP(a) In an experiment, what is the rule for when to make a bar graph? (b) Define these scales. (c)What is the rule for when to make a line graph? (d)Define these scales.For the following experimental results, interpret specifically the relationship between the independent and dependent variables:(a) If you participated in the study in question 21 and had been deprived of 5 hours of sleep, how many errors do you think you would have made? (b) If we tested all people in the world after 5hours of sleep deprivation, how many errors do you think each would make? (c) What symbol stands for your prediction in part b?23SP24SP25SPIn a study of participants speeds of texting, the researchers concluded, We found a difference between the three means for the three age groups, with slower speeds occurring with increased age. However, no speed differences were found between the overall means for males and females. Based on this conclusion, describe the relationship we expect to find in nature between texting speed and (a) age; (b) gender.What does a larger measure of variability communicate about: (a) the size of differences among the scores in a distribution? (b) how consistently the participants behaved? (c) how spread out the distribution is?In any research, why is describing the variability important?Thinking back on the previous three chapters, what are the three major pieces of information we need to know to summarize a distribution?4SP(a) What is the range? (b) Why is it not the most accurate measure of variability? (c) When is it primarily used?6SP7SPWhy is the mean a less accurate description of the distribution if the variability is large than if it is small?9SP(a) What do S2 X, s2 X, and s2 X have in common? (b)How do they differ in their use?(a) How do we determine the scores that mark the middle 68% of a sample? (b) How do we determine the scores that mark the middle 68% of a known population? (c) How do we estimate the scores that mark the middle 68% of an unknown population?Why are your estimates of the population variance and standard deviation always larger than thecorresponding values that describe a sample from that population?In a condition of an experiment, a researcher obtains the following scores: 3 2 1 0 7 4 8 6 6 4 Determine the following: (a) the range, (b) the variance, (c) the standard deviation, (d) the two scores between which 68% of the scores lie.If you could test the entire population in question 13, what would you expect each of the following to be? (a) The typical, most common score; (b) the variance; (c) the standard deviation; (d) the two scores between which 68% of the scores lie.Tiffany has a normal distribution of scores ranging from 2 to 9. (a) She computed the variance to be 2.06. What should you conclude about this answer and why? (b) She recomputes the standard deviation to be 18. What should you conclude and why? (c) If she computed that SX 0, what would this indicate?From his statistics grades, Demetrius has a X 60 and SX 20. Andrew has X 60 and SX 8. (a)Who is the more inconsistent student and why? (b)Who is more accurately described as a 60 student and why? (c) For which student can you more accurately predict the next test score and why? (d)Who is more likely to do either extremely well or extremely poorly on the next exam and why?17SPSay that you conducted the experiment in question17 on the entire population. (a)Summarize the relationship that youd expectto observe. (b)Compute how consistently youd expect participants to behave in each condition.In two studies, the mean is 40 but in Study A, SX=5, and in Study B, SX=10. (a) What is the difference in the appearance of the distributions from these studies? (b) Where do you expect the majority of scores to fall in each study?Consider these normally distributed ratio scores from an experiment: (a) What should you do to summarize the experiment? (b) Summarize the relationship in the sample data. (c) How consistent are the scores in each condition?21SP(a) What are the symbols for the true population variance and standard deviation? (b) What are the symbols for the biased estimators of the variance and standard deviation? (c) What are the symbols for the unbiased estimators of the variance and standard deviation? (d) When do we use the unbiased estimators? When do we use the biased estimators?For each of the following, indicate the conditions of the independent variable, the scores from which variable to analyze, whether it is appropriate to compute the mean and standard deviation, and the type of graph you would create. (a) We test whether participants laugh longer (in seconds) at jokes told on a sunny or a rainy day. (b) We compare groups who have been alcoholics for 1, 3, or 5 years. In each, we measure participants income. (c) We count the number of creative ideas produced by participants who slept either 6, 7, or 8 hours the night before.24SP1SPWhat two factors determine the size of a z -score?3SPWhy are z-scores called standard scores?5SPAn instructor says that your test grade produced a very large positive z -score. (a) How well did you do on the test? (b) What do you know about your raw scores relative frequency? (c) What does it mean if you scored at the 80th percentile? (d) What distribution would the instructor examine to make the conclusion in part c?7SP8SP9SP10SP11SPIn a normal distribution, what proportion of all scores would fall into each of the following areas? (a) between the mean and z=+1.89; (b) below z=2.30; (c) between z=1.25 and z=+2.75; (d) above z=+1.96 and below 1.96For a distribution, X=100,Sx=16, and N=500. (a) What is the relative frequency of scores between 76 and the mean? (b) How many participants are expected to score between 76 and the mean? (c) What is the percentile of someone scoring 76? (d) How many participants are expected to score above 76?(a) What is a sampling distribution of means? (b) How do we use it? (c) What do we mean by the underlying raw score population?15SP16SP17SP18SP19SP20SP21SPFor the diagnostic test in problem 21, we want to create the sampling distribution of means when N=64. (a) What does this distribution show? (b) What is the shape of the distribution and what is its ? (c) Calculate x for this distribution. (d) What is your answer in part c called, and what information does it provide? (e) Determine the relative frequency of sample means above 77.23SPSuppose you own shares of a companys stock. Over the past 10 trading days, its mean selling price has been $14.89. For the history of the company, the average price of the stock has been $10.43 (with x=5.60). You wonder if the mean selling price for the next 10 days can be expected to get much higher. Should you wait to sell, or should you sell now?25SP26SP1SP2SP3SP4SP5SPFour airplanes from different airlines have crashed in the past two weeks. This terrifies Megan, who must travel on a plane. Her travel agent claims that the probability of a plane crash is minuscule. Who is correct and why?7SP8SP9SPWhat is the difference between using both tails versus one tail of the sampling distribution in terms of (a) the region of rejection? (b) the critical value?
11SP12SP13SP14SP15SP16SP17SP18SP19SP20SP21SP22SP23SP24SP25SP1SP2SP3SP4SP5SP6SP7SP8SP9SP10SP11SP12SP13SP14SP15SP16SP17SP18SP19SP20SP21SP22SP23SP24SP25SP1SP2SP3SP4SP5SP6SP7SP8SP9SP10SP11SPA researcher predicts that smoking cigarettes decreases a persons sense of smell. On a test of olfactory sensitivity, the for nonsmokers is 18.4. A sample of 12 people who smoke a pack a day produces X=16.25,sx2=4.75. (a) What are H0 and Ha for this study? (b) Compute tobt. (c) What is your tcrit? (d) What should the researcher conclude about this relationship? (e) Report your results using the correct format. (f) Compute the confidence interval for if appropriate.13SP14SP15SP16SP17SP18SP19SP20SP21SP22SP23SP24SP25SP1SP2SP3SP4SP5SP6SP7SP8SP9SP10SP11SP12SP13SP14SP15SP16SP17SP18SP19SP20SP21SP22SP23SP24SP25SP1SP2SP3SP4SP5SP6SP7SP8SP9SP10SP11SP12SP13SP14SP15SP16SP17SP18SP19SP20SP21SP22SP23SP24SP25SP1SP2SP3SP4SP5SP6SP7SP8SP9SP10SP11SP12SP13SP14SP15SP16SP17SP18SP19SP20SP21SP22SP23SP24SP25SP1SP2SP3SP4SP5SP6SP7SP8SP9SP10SP11SP12SP13SP14SP15SP16SP17SP18SP19SPYou measure the dependent variable of participants relaxation level as a function of whether they meditated before being tested, and whether they were shown a film containing a low, medium, or high amount of fantasy. Here are the data and the ANOVA. Amount of Fantasy Low Medium High Mediation 5 7 9 6 5 8 2 6 10 2 9 10 5 5 10 No Mediation 10 2 5 10 5 6 9 4 5 10 3 7 10 2 6 Source Sum of Squares df Mean Square F A: Fantasy 42.467 2 21.233 13.134 B: Mediation .833 1 .833 .515 AB: Interaction 141.267 2 70.633 43.691 Within 38.800 24 1.617 Total 223.367 29 (a) Which effects are significant? (b) Compute the main effect means and the interaction means. (c) Perform the Tukey HSD test where appropriate. (d) What do you conclude about the relationship(s) this study demonstrates? (e) Evaluate the impact of each effect.21SP22SP23SP24SP