1. [16 points] A coach uses a nw technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores were recorded before and after the training. The results are shown below.

Before After

9.7 9.9

9.4 9.7

9.6 9.2

9.6 9.4

9.6 9.7

9.7 10.0

9.4 9.2

Using a 0.05 level of significance, test the claim that the training technique is effective in raising the gymnasts’ scores.

Ho:

Ha:

Test Statistic:

p-value:

Decision:

Conclusion:

2.[12 pts] A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a 90% confidence interval for the difference in blood pressure. Can you conclude that the diet helped? (Assume the two samples are independent and have been randomly selected.)

Treatment Group Control Group

n=85 n=51

mean=189.1 mean=203.7

s=38.7 s=37.2

3.[16 pts] A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 30 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 20 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal. (Assume the samples are independent and have been randomly selected.)

Ho:

Ha:

Test Statistic:

Pvalue:

Decision:

Conclusion:

4.[14 pts] Managers rate employees according to job performance and attitude. The results for several randomly selected employees are shown below.

Performance Attitude

____________ ______________

59 72

63 67

65 78

69 82

58 75

77 87

76 92

69 83

70 87

64 78

a). Use a 0.05 significance level to test for a linear correlation between attitude and performance.

Ho:

Ha:

Test Statistic:

Critical Value(s):

Decision:

Conclusion:

b) What percentage of the variation in performance can be explained by the linear relationship?

c) Find the equation of the regression line that expresses performance (y) in terms of attitude (x).

d) What is the best predicted performance rating for a person whose attitude rating is 80?

5.[16 pts] In studying the responses to a multiple-choice test question, the following sample data were obtained. At the .05 significance level, test the claim that the responses occur with the same frequency.

(Show all calculations necessary to calculate the test statistic.)

Response Frequency

A 11

B 15

C 17

D 18

E 19

Ho:

Ha:

Test Statistic:

Pvalue:

Decision:

Conclusion:

6. [16 pts] A case-control study was conducted to investigate a relationship between colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are summarized below. Test the claim that injuries are independent of helmet color, using a .05 level of significance. Should motorcycle drivers chose helmets with a particular color? If so, which color appears best?

Black White Yellow/Orange Red Blue

Controls (not injured) 481 394 30 167 58

Cases (injured or killed) 198 120 5 73 27

7. [10 pts] Below are data from the 1st and 2nd exams in this class. Find the best model. Consider only linear, quadratic, logarithmic, exponential, and power models. Indicate r2 for each model.

Exam 1(X) Exam 2(Y)

69 92.5

87 90

51 71.5

43.5 30

93 93

91 71.5

96 97

98.5 96.5

84 96.5

97 93.5

73 60

82.5 56

83 83.5

85 73.5

93 79

96 97

40 30.5

82 81

89 73

64.5 31

90 97

35 29

83 77

82 38

Before After

9.7 9.9

9.4 9.7

9.6 9.2

9.6 9.4

9.6 9.7

9.7 10.0

9.4 9.2

Using a 0.05 level of significance, test the claim that the training technique is effective in raising the gymnasts’ scores.

Ho:

Ha:

Test Statistic:

p-value:

Decision:

Conclusion:

2.[12 pts] A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a 90% confidence interval for the difference in blood pressure. Can you conclude that the diet helped? (Assume the two samples are independent and have been randomly selected.)

Treatment Group Control Group

n=85 n=51

mean=189.1 mean=203.7

s=38.7 s=37.2

3.[16 pts] A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 30 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 20 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal. (Assume the samples are independent and have been randomly selected.)

Ho:

Ha:

Test Statistic:

Pvalue:

Decision:

Conclusion:

4.[14 pts] Managers rate employees according to job performance and attitude. The results for several randomly selected employees are shown below.

Performance Attitude

____________ ______________

59 72

63 67

65 78

69 82

58 75

77 87

76 92

69 83

70 87

64 78

a). Use a 0.05 significance level to test for a linear correlation between attitude and performance.

Ho:

Ha:

Test Statistic:

Critical Value(s):

Decision:

Conclusion:

b) What percentage of the variation in performance can be explained by the linear relationship?

c) Find the equation of the regression line that expresses performance (y) in terms of attitude (x).

d) What is the best predicted performance rating for a person whose attitude rating is 80?

5.[16 pts] In studying the responses to a multiple-choice test question, the following sample data were obtained. At the .05 significance level, test the claim that the responses occur with the same frequency.

(Show all calculations necessary to calculate the test statistic.)

Response Frequency

A 11

B 15

C 17

D 18

E 19

Ho:

Ha:

Test Statistic:

Pvalue:

Decision:

Conclusion:

6. [16 pts] A case-control study was conducted to investigate a relationship between colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are summarized below. Test the claim that injuries are independent of helmet color, using a .05 level of significance. Should motorcycle drivers chose helmets with a particular color? If so, which color appears best?

Black White Yellow/Orange Red Blue

Controls (not injured) 481 394 30 167 58

Cases (injured or killed) 198 120 5 73 27

7. [10 pts] Below are data from the 1st and 2nd exams in this class. Find the best model. Consider only linear, quadratic, logarithmic, exponential, and power models. Indicate r2 for each model.

Exam 1(X) Exam 2(Y)

69 92.5

87 90

51 71.5

43.5 30

93 93

91 71.5

96 97

98.5 96.5

84 96.5

97 93.5

73 60

82.5 56

83 83.5

85 73.5

93 79

96 97

40 30.5

82 81

89 73

64.5 31

90 97

35 29

83 77

82 38

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