Question

A pharmaceutical company believes its Alzheimer’s drug may have an effect on cortical atrophy. If it
decreases cortical atrophy, it may be a promising candidate for further drug trials; if it increases cortical
atrophy, it may provide insight into the mechanism of Alzheimer’s disease. Thus the company decides
to test the drug on rats, as either result may hold future benefits.
Among 115 transgenic rats (genetically engineered to induce Alzheimer’s), 65 rats receive the drug over
6 months, 50 rats are given placebo, and all rats’ brains are sectioned and stained to measure cortical
atrophy after 6 months. The mean cortical atrophy is 0.25 mm among the rats receiving the drug; the
mean cortical atrophy is 0.29 mm among the rats on placebo.
Suppose that the rats who took the drug had a sample standard deviation of 0.08 and the control rats
had a sample standard deviation of 0.11. Does the mean cortical atrophy differ between the rats who
took the drug and the rats who were on placebo? Test the company’s claim at the α = 0.05 level.
(a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret
them in context of the problem)
(b) Draw a picture of the distribution of the test statistic under H o . Label and provide values for the
critical value and the test statistic, and shade the critical region. (You may want to complete parts
c and d first)
(c) Calculate the test statistic
(d) Calculate the critical value
(e) Make and justify a statistical decision at the α = 0.05 level.
(f) State your conclusions in context of the problem.
(g) Construct a 95% confidence interval for the true difference in cortical atrophy between rats who
took the drug and rats who took the placebo.
(h) Does this interval reaffirm your statistical decision from the hypothesis test? Explain.

Answer 1

Let , X: Cortial atrophy among the rats receiving the drug Y: Cortial atrophy among the rats on placebo