28. Alzheimer's. Testing for Alzheimer's disease can be a long and expensive process, consisting of lengthy test and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior citizens. A patient who tested positive would then go through the more expensive battery of test and medical diagnosis. The authors reported a false-positive rate of 4% and a false-negative rate of 8%.

a) Put this in the context of a hypothesis test. What are the null and alternative hypotheses?

b) What would a Type I error mean?

c) What would a Type II error mean?

d) Which is worse here, a Type I or Type II error? Explain.

e) What is the power of this test?