78. Recall the data from Example 10.4 about the experiment in the low-level college mathematics course.

Here again are the 85 nal exam scores for those in the experimental group (E) and the 79 nal exam scores for those in the control group (C):

E: 34 27 26 33 23 37 24 34 22 23 32 5 30 35 28 25 37 28 26 29 22 33 31 23 37 29 0 30 34 26 28 27 32 29 31 33 28 21 34 29 33 6 8 29 36 7 21 30 28 34 28 35 30 34 9 38 9 27 25 33 9 23 32 25 37 28 23 26 34 32 34 0 24 30 36 28 38 35 16 37 25 34 38 34 31 C: 37 22 29 29 33 22 32 36 29 6 4 37 0 36 0 32 27 7 19 35 26 22 28 28 32 35 28 33 35 24 21 0 32 28 27 8 30 37 9 33 30 36 28 3 8 31 29 9 0 0 35 25 29 3 33 33 28 32 39 20 32 22 24 20 32 7 8 33 29 9 0 30 26 25 32 38 22 29 29

a. Determine a 95% con dence interval for the difference of population means using the z method given in Section 10.1.

b. Obtain a bootstrap sample of 1000 differences of means. Check the bootstrap distribution for normality using a normal probability plot.

c. Use the standard deviation of the bootstrap distribution along with the mean and t critical value from

(a) to get a 95% con dence interval for the difference of means.

d. Use the bootstrap sample and the percentile method to obtain a 95% con dence interval for the difference of means.

e. Compare your three con dence intervals. If they are very similar, why do you think this is the case?

In the light of your results for

(c) and (d), does the z method of

(a) seem to work, regardless of normality?

Explain.

f. Are your results consistent with the results of Example 10.4? Explain.