Recall the drug experiment in Examples 8.3 and 8.5, in which we tested to determine whether the mean response time for rats injected with a drug differs from the control mean response time of m = 1.2 seconds. The test setup is repeated here:

H0: m = 1.2 Ha: m  1.2 1i.e., m 6 1.2 or m 7 1.22 LO9 Test statistic: z =

x - 1.2 sx Rejection region: z 6 -1.96 or z 7 1.96 for a = .05 z 6 -2.575 or z 7 2.575 for a = .01 Note that two rejection regions have been specified, corresponding to values of a = .05 and a = .01, respectively. Assume that n = 100 and s = .5.

a. Suppose drug-injected rats have a mean response time of 1.1 seconds; that is, m = 1.1. Calculate the values of b corresponding to the two rejection regions.
Discuss the relationship between the values of a and b.

b. Calculate the power of the test for each of the rejection regions when m = 1.1.