TEXT BOOK (ISBN10: 1111837260) ====9781111837266 Understanding Statistics in the Behavioral Sciences Pagano, Robert R. 1. Chapter Six # 10, 15, 18, 22 2. Chapter Seven # 9, 12, 13,18, 1. Chapter Six # 10, 15, 18, 22 Linear Correlation 10). The Pearson and Spearman rho correlation coefficients are related. a). Is this statement correct? b). Explain 15). In large introductory sociology course, a professor gives two exams. The professor want to determine whether the scores students receive on the second exam are correlated with scores on the first exam. To make the calculation easier a sample of eight students is selected. Their scores are shown in the accompanying table. Student Exam 1 Exam 2 1 60 60 2 75 100 3 70 0 8 4 72 8 6 5 54 3 7 6 83 7 9 7 80 5 8 8 65 0 9 a). Construct a scatter plot of the data, using exam 1 score as the X variable. Does the relationship look linear? b). Assuming a linear relationship exists between scores on the two exams, compute the value for Pearson c). How well does the relationship account for the score on exam 2? 18).Am educator has constructed a test for mechanical aptitude. He wants to determine how reliable the test is over two administration spaced by 1 month. A study is conducted in which 10 students are given two administrations of the test, with the second administration being 1 month after the first. The data are given in the following table. Studen t Administration 1 Administration 2 10 1 0 1 10 2 2 1 15 3 0 2 17 4 5 2 25 5 7 2 32 6 5 3 37 7 3 4 40 8 0 4 38 9 2 3 30 10 47 49 a). Construct a scatter plot of the paired scores. b). Determine the value of . c).Would it be fair to say that this is a reliable test? Explain using 2 22). A social psychologist conducts a study to determine the relation between religion and self esteem. Ten eight graders are randomly selected for the study. Each individual undergoes two tests, one measuring selfesteem and the other religious involvement. For the selfesteem test, the lower the score is, the higher self esteem is; for the test measuring religious involvement, the higher the score is, the higher religious involvement is. The self esteem has a range from 1 to 10 and the religious involvement test ranges from 0 t0 50. For the purpose of this question, assume both tests are well standardized and if interval scaling. The following data are collected. Subject Religious Self esteem Involvement 1 5 8 2 25 3 3 45 2 4 20 7 5 30 5 6 40 5 7 1 4 8 15 4 9 10 7 10 35 3 a). If a relationship exists such that the more religiously involved one is, the higher actual self esteem is, would you expect computed on the provided values to be negative of positive? Exaplain b).Compute . Were you correct in your answer to part a? Chapter Seven # 9, 12, 13,18 . Chapter 7 # 9, 12, 13, 18 Linear Regression 9). Given the set of paired X and Y score, X 7 Y 1 10 2 9 4 13 3 7 3 11 4 13 5 A). Construct a scatter plot of the paired scores. Does the relationship appear linear? b). Determine the least square regression line for predicting Y given X c). Draw the regression line on the scatter plot. d).Using the relationship between X and Y what would you predict for Y if X=12? (round to two decimal places). 12).A statistics professor conducts a study to investigate the relationship between the performance of his students on exams and their anxiety. Ten students from his class are sel3ected for the experiment. Just before taking the final exam, the 10 students are given an anxiety questionnaire. Here are final exam and anxiety scores for the 10 students: Studen t No. Anxiety Final exam 1 2 3 4 5 6 7 8 9 2 8 8 2 4 1 5 8 3 5 6 3 3 9 8 9 3 1 9 2 4 2 6 4 5 0 5 5 4 6 7 0 4 5 5 1 1 0 3 7 7 2 a). On a piece of graph paper, construct a scatter plot of the paired score. Use anxiety as the X variable. b). Describe the relationship shown on the graph c). Assuming the relationship is linear, compute the value of of Pearson r d). Determine the least squares regression line for predicting the final exam score, given the anxiety level. Should by be positive or negative? Why? e). Draw the least square regressiomn line of part (d) on the scatter plot of part (a) f). Based on the data of 10 students, if a student has anxiety score of 38, what value would you predict for her final exam score (round to two decimal places) g). Calculate the standard error of estimate for predicting final exam scores from anxiety scores 13). The sales manager of a large sporting goods store has recently started a national advertising campaign. He has kept a record of the monthly costs of the advertising and the monthly profits. These are shown here. There entries are in thousands of dollars. month Monthly advertisin g cost Monthly profit Jan 10.0 Feb 14.0 Mar 11.4 Apr 15.6 May 16.8 Jun 11.2 Jul 13.2 125 200 160 150 210 110 125 a). Assuming a line relationship exists, derive the least squares regression line for predicting monthly profits from monthly advertising costs. b). In August, the manager plans to spend $17,000 on advertising. Based on the data, how much profit should he expect that month? (Round to the nearest 1000.) Thou c). Given the relationship shown by the paired scores, can you think of a reason why manager doesn't spend a lot more money on advertising? 18). In Chapter 6, problem 22 (P. 153), data were presented from a study conducted to determine the relationship between religious involvement and self esteem. Tha data are again presented below. Subject Religious Self esteem Involvement 1 5 8 2 25 3 3 45 2 4 20 7 5 30 5 6 40 5 7 1 4 8 15 4 9 10 7 10 35 3 a). Assuning a linear relationship, derive the least squares regression line predicting self esteem from religious involvement. b). Using this regression line, what value of self esteem would you predict for an eighth grader whose value of religious involvement is 43? TEXT BOOK (ISBN10: 1111837260) ====9781111837266 Understanding Statistics in the Behavioral Sciences Pagano, Robert R