A research neurologist is testing the effect of a drug on response time by injecting 100 rats with a unit dose of the drug, subjecting each rat to a neurological stimulus and recording its response time

The neurologist knows that the mean response time for rats not injected with the drug (the "control" rats) is 1.2 seconds. She wishes to conduct the following test (i.e. determine if the mean response time for drug injected rats differs from 1.2 seconds).

????o: ???? = 1.2 (The drug has no effect) vs. ????????: ???? 1.2 (The drug has an effect)

The null hypothesis will be rejected if the average response time from the sampled rats is either smaller than 1.1 seconds or greater than 1.3 seconds. Assume ???? = 0.5 seconds.

(a) Find the type I error rate, ????

(b) If the drug-injected rats have a mean response time of 1 seconds, what is the power of the test?