Refer to the previous exercise about medical diagnoses. A New York Times article (February 17, 1999) about the PSA blood test for detecting prostate cancer stated: “The test fails to detect prostate cancer in 1 in 4 men who have the disease.”
a. For the PSA test, explain what a Type I error is, and explain the consequence to a man of this type of error.
b. For the PSA test, what is a Type II error? What is the consequence to a man of this type of error?
c. To which type of error does the probability of 1 in 4 refer?
d. The article also stated that if you receive a positive result, the probability that you do not actually have prostate cancer is 2/3. Explain the difference between this and the conditional probability of a Type I error, given that you do not actually have prostate cancer.