4. Professor Taylor do es a n experiment and establishes that a…4. Professor Taylor do es a n experiment and establishes that a correlation exists between variables A and B. On the basis of this correlation, she asserts that A is the cause of B. Is this assertion correct? Explain. 8. A study has shown that the correlation between fatigue and irritability is 0.53. On the basis of this correlation, the author concludes that fatigue is an important factor in producing irritability. I s t his conclusion justified? Explain 9. What factors influence the choice of whether to use a particular correlation coefficient? Give some examples. 11. When two variables are correlated, there are f our possible explanations of the correlation. What are they? 12. What effect might a n extreme score have on the magnitude of relationship between two variables? Discuss. 17. A researcher conducts a study to investigate the relationship between cigarette smoking and illness. The number of cigarettes smoked daily and the number of days absent from work in the last year due to ill[1]ness is determined for 12 individuals employed at the company where the researcher works. The scores are given in the following table. Subject Cigarettes Smoked Days Absent 101 203 308 4 10 10 5 13 4 6 20 14 7 27 5 8 35 6 9 35 12 10 44 16 11 53 10 12 60 16 a. Construct a scatter plot for these data. Does the relationship look linear? b. Calculate the value of Pearson r. c. Eliminate the data from subjects 1, 2, 3, 10, 11, and 1 2. This de creases the range of both variables. Recalculate r f or the remaining subjects. What effect does decreasing the range have on r? d. If you use the full set of scores, what percentage of the variability in the number of days absent is accounted for by the number of cigarettes smoked daily? Of what use is this value? 19. A group of researchers has devised a stress questionnaire consisting of 15 life events. They are interested in determining whether there is c ross[1]cultural agreement on the re lative amount of adjustment each eventen tails. The questionnaire is given to 30 0 Americans and 300 Italians. Each individual is instructed to use the event of “marriage” as the standard and to judge each of the other life events in relation to the adjustment required in marriage. Marriage is arbitrarily given a value of 50 points. If an event is judged to require greater adjustment than marriage, the e vent should receive more than 50 points. How many more points depends on how much more adjustment is required. After each subject within each culture has assigned points to the 15 life events, the points for each event are averaged. The results are shown in the following table. Life Event Americans Italians Death of spouse 100 80 Divorce 73 95 Marital separation 65 85 Jail term 63 52 Personal injury 53 72 Marriage 50 50 Fired from work 47 40 Retirement 45 30 Pregnancy 40 28 Sex difficulties 39 42 Business readjustment 39 36 Trouble with in-laws 29 41 Trouble with boss 23 35 Vacation 13 16 Christmas 12 1 b. Assume the data are only of ordinal scaling and compute the correlation between ratings o f t he two cultures 20. Given the following set of paired scores from ive subjects, Subject No. 1 2 3 45 Y 5 6 9 911 X 6 8 4 8 7 a. Construct a scatter plot of the data. b. Compute the value of Pearson r. c. Add the following paired scores from a sixth subject to the data: Y [1] 26, X [1] 25. d. Construct another scatter plot, this time for the six paired scores. e. Compute the value of Pearson r for the six paired scores. f. Is there much o f a difference between your answers for parts b and e? Explain the difference 4. For this problem, let’s suppose that you are a psychologist employed I n t he human resources department of a large corporation. The corporation president has just finished talking with you about the importance of hiring productive personnel in the manufacturing section of the corporation and has asked you to help improve the corporation’s ability to do so. There are 300 employees in this section, with each employee making the same item. Until n ow, the corporation has been depending solely on interviews for selecting these employees. You search the literature and discover two well-standardized paper & pencil performance tests that you think might be related to the performance requirements of this section. To deter[1]mine whether e ither might be used as a screening device, you select 10 representative employees from the manufacturing section, making sure that a wide range of performance is represented i n the sample, and administer the two tests to each employee. The data are shown in the table. The higher the score, the better the performance. The work performance scores are the actual number of items completed by each employee per week, averaged over the past 6 months. a. Construct a scatter plot of work performance and test 1, using test 1 a s t he X variable. Does the relationship look linear? b. Assuming i t is linear, compute the value of Pearson r. c. Construct a scatter plot of work performance and test 2, using test 2 a s the X variable. Is the relationship linear? d. Assuming it is linear, compute the value of Pear[1]son r. e. If you could use only one o f t he t wo tests f or screening prospective employees, would you use either test? If yes, which one? Explain. Employee12345678910Work performance 50 74 62 90 98 52 68 80 88 76Test 1 10 19 20 20 21 14 10 24 16 14Test 2 25 35 40 49 50 29 32 44 46 35 MathStatistics and Probability PSYC 2f23

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