74. Can the right diet help us cope with aging-related diseases such as Alzheimer s disease? A study ( Reversals of Age-Related Declines in Neuronal Signal Transduction, Cognitive, and Motor Behavioral De cits with Blueberry, Spinach, or Strawberry Dietary Supplement, J. Neurosci., 1999; 8114—8121)
investigated the effects of fruit and vegetable supplements in the diet of rats. The rats were 19 months old, which is aged by rat standards. The 40 rats were randomly assigned to four diets, of which we will consider just the blueberry diet and the control diet here. After eight weeks on their diets, the rats were given a number of tests. We give the data for just one of the tests, which measured how many seconds they could walk on a rod. Here are the times for the ten control rats (C) and ten blueberry rats (B):
C: 15.00 7.00 2.44 5.60 3.63 6.24 4.12 8.21 3.90 0.95 B: 5.12 9.38 18.77 15.03 6.67 7.91 7.38 15.09 11.57 8.98 The objective is to obtain a 95% con dence interval for the difference of population means.

a. Determine a 95% con dence interval for the difference of population means using the method based on the theorem of Section 10.2.

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?
If you had used a critical value from the normal table rather than the t table,would the result of (c)
agree better with the result of (d)? Why?

f. Interpret your results. Do the blueberries make a substantial difference?