Applied Statistics and Probability for Engineers

11-11 CORRELATION 405

with 0.05. We can compute the t-statistic of Equation 11-46 as

This statistic is also reported in the Minitab output as a test of H 0 :  1  0. Because t0.025,23

2.069, we reject H 0 and conclude that the correlation coefficient  0.

Finally, we may construct an approximate 95% confidence interval on from Equation

10-57. Since arctanh rarctanh 0.98182.3452, Equation 11-50 becomes

which reduces to

EXERCISES FOR SECTION 11–10

0.95850.9921

tanh a2.3452

1.96

122

btanh a2.3452

1.96

122

b

t 0 

r 1 n   2

21   r^2



0.9818 123

11   0.9640

24.8

11-55. The final test and exam averages for 20 randomly

selected students taking a course in engineering statistics and a

course in operations research follow. Assume that the final av-

erages are jointly normally distributed.

(a) Find the regression line relating the statistics final average

to the OR final average.

(b) Test for significance of regression using 0.05.

Statistics 86 75 69 75 90

OR 80 81 75 81 92

Statistics 94 83 86 71 65

OR 95 80 81 76 72

Statistics 84 71 62 90 83

OR 85 72 65 93 81

Statistics 75 71 76 84 97

OR 70 73 72 80 98

(c) Estimate the correlation coefficient.

(d) Test the hypothesis that 0, using 0.05.

(e) Test the hypothesis that 0.5, using 0.05.

(f ) Construct a 95% confidence interval for the correlation

coefficient.

11-56. The weight and systolic blood pressure of 26 ran-

domly selected males in the age group 25 to 30 are shown in

the following table. Assume that weight and blood pressure

are jointly normally distributed.

(a) Find a regression line relating systolic blood pressure to

weight.

(b) Test for significance of regression using 0.05.

(c) Estimate the correlation coefficient.

(d) Test the hypothesis that 0, using 0.05.

(e) Test the hypothesis that 0.6, using 0.05.

(f) Construct a 95% confidence interval for the correlation

coefficient.

11-57. Consider the NFL data introduced in Exercise 11-4.

(a) Estimate the correlation coefficient between the number of

games won and the yards rushing by the opponents.

(b) Test the hypothesis H 0 : 0 versus H 1 : 0 using

0.05. What is the P-value for this test?

(c) Construct a 95% confidence interval for .

(d) Test the hypothesis H 0 :     0.7 versus H 1 :  0.7

using 0.05. Find the P-value for this test.

Systolic

Subject Weight BP

1 165 130

2 167 133

3 180 150

4 155 128

5 212 151

6 175 146

7 190 150

8 210 140

9 200 148

10 149 125

11 158 133

12 169 135

13 170 150

Systolic

Subject Weight BP

14 172 153

15 159 128

16 168 132

17 174 149

18 183 158

19 215 150

20 195 163

21 180 156

22 143 124

23 240 170

24 235 165

25 192 160

26 187 159

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