# Project #47332 - Statistics

Complete in Microsoft Word. Show all workings to the answer.

1. The Pearson r and Spearman rho correlation coefficients are related. Is this statement correct? Explain.

2. 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

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 r.

c. How well does the relationship account for the scores on exam 2? Education

3. An educator has constructed a test for mechanical aptitude. 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 administration being 1 month after the first. The data are given in the following table.

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

4. 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 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 test has a range from 1 to 10 and the religious

involvement test ranges from 0 to 50. For the purposes of this question, assume both tests are

well standardized and of interval scaling. The following data 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

a.     If a relationship exists such that the more religiously

5. 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

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.)

6. 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 bY 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 final exam score? (Round to two decimal places.)

g. Calculate the standard error of estimate for predicting final exam scores from anxiety scores.

clinical, health, education

7. 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.

10.0     14.0      11.4     15.6    16.8    11.2    13.2

Monthly Profit

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? I/O

8. In Chapter 6, Problem 22 (p. 153), data were presented from a study conducted to determine the relationship between religious involvement and self-esteem. The data are again presented below.

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

a. Assuming a linear relationship, derive the least squares regression line for 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? social, developmental

 Subject Mathematics Due By (Pacific Time) 11/13/2014 03:00 pm
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