For the data of the previous exercise, we now want to test the hypothesis of equal population means.

Data from in previous exercise 

a. Carry out a two-tailed test using the two sample t test. Although this test requires normal data, it will still work pretty well for moderately nonnormal data. Nevertheless, you should check the data for normality to see if the test is justified.

b. Carry out a two-tailed permutation test for the hypothesis of equal population means.

c. Compare the results of (a) and (b). Would you expect them to be similar for the data of this problem? Discuss their relationship to the results of the previous exercise. Summarize your conclusions about the effectiveness of blueberries.

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84. Can the right diet help us cope with dis- eases associated with aging such as Alz- heimer's disease? A study ("Reversals of Age-Related Declines in Neuronal Signal Transduction, Cognitive, and Motor Behavioral Deficits with Blueberry, Spi- nach, or Strawberry Dietary Supplement," J. Neurosci. 1999: 8114-8121) investigated the effects of fruit and vegetable supple- ments in the diet of rats. The rats were 19 months old, which is aged by rat stan- dards. The 40 rats were randomly assigned to four diets, of which we will consider just the blueberry diet and the control diet here. After 8 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: B: 15.00 6.24 5.12 7.91 7.00 4.12 9.38 7.38 2.44 8.21 18.77 15.09 5.60 3.90 15.03 11.57 3.63 0.95 6.67 8.98