Prostate cancer. Prostate cancer is the most common type of cancer found in men. Physicians routinely perform a Prostate-Specific Antigen (PSA) test to determine whether there is any evidence of prostate cancer. A patient who tested positive would then go then through an expensive biopsy that costs approximately $1000 and which is not covered by some medical plans. Studies have shown that the test is not very accurate. The false positive rate is 13.5%, and the false negative rate is almost 30%.

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?