Chapter 6 15. In a large introductory sociology course, a professor gives two exams. The professor wants to determine whether the scores students receive on the second exam are correlated with their...

Chapter 6


15. In a large introductory sociology course, a professor gives two exams. The professor wants to determine whether the scores students receive on the second exam are correlated with their scores on the first exam. To make the calculations 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 80
4 72 68
5 54 73
6 83 97
7 80 85
8 65 90

1. Construct a scatter plot of the data, using exam1 score as the X variable. Does the relationshiplook linear?


2. Assuming a linear relationship exists betweenc. scores on the two exams; compute the value forPearson r.

1. How well does the relationship account for thescores on exam 2?

18.
An educator has constructed a test for mechanicalaptitude. He wants to determine how reliable the
test is over two administrations spaced by 1 month.A study is conducted in which 10 students are given
two administrations of the test, with the second administrationbeing 1 month after the first. The data
are given in the following table.

Student Administration 1 Administration 2

1 10 10
2 12 15
3 20 17
4 25 25
5 27 32
6 35 37
7 43 40
8 40 38
9 32 30
10 47 49

a.
Construct a scatter plot of the paired scores.

b.
Determine the value of
r.


c. Would it be fair to say that this is a reliable test?
Explain using
r^2

22-A social psychologist conducts a study to determine the relationship between religion and self-esteem.Ten eighth graders are randomly selected for the study. Each individual undergoes two tests,one measuring self-esteem and the other religious involvement. For the self-esteem test, the lower thescore is, the higher self-esteem is; for the test measuringreligious involvement, the higher the scoreis, the higher religious involvement is. The self-esteemtest has a range from 1 to 10 and the religiousinvolvement test ranges from 0 to 50. For thepurposes of this question, assume both tests arewell standardized and of interval scaling. The followingdata are collected.
Subject Religious Involvement Self-Esteem
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

Chapter 7

9. Given the set of paired X and Y scores,
X 7 10 9 13 7 11 13
Y 1 2 4 3 3 4 5

x	y	Xy	X2
7	1	7	49
10	2	20	100
9	4	36	81
13	3	39	169
7	3	21	49
11	4	44	121
13	5	65	169
Totals 70	22	232	738

a.Construct a scatter plot of the paired scores. Does the relationship appear linear?
b. Determine the least-squares 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 value 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 selected 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:
Student No. 1 2 3 4 5 6 7 8 9 10
Anxiety 28 41 35 39 31 42 50 46 45 37
Final Exam 82 58 63 89 92 64 55 70 51 72
a.On a piece of graph paper, construct a scatter plot of the paired scores. Use anxiety as the X variable.
b. Describe the relationship shown in the graph.
c. Assuming the relationship is linear, compute the value of Pearson r
d. Determine the least-squares regression line for predicting the final exam score, given the anxiety level. Should b y be positive or negative? Why?
e. Draw the least-squares regression line of part d on the scatter plot of part a.
f. Based on the data of the 10 students, if a student has an anxiety score of 38, what value would you predict for her fi al 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.
The entries are in thousands of dollars
Month Jan. Feb. Mar. Apr. May Jun. Jul.
Monthly
Advertising 10.0 14.0 11.4 15.6 16.8 11.2 13.2
Cost
Monthly 125 200 160 150 210 110 125
a. Assuming a linear 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.)
c. Given the relationship shown by the paired scores, can you think of a reason why the manager doesn’t spend a lot more money on advertising?