A medical manufacturer claims that its test for MRSA has an accuracy rate of 92%. In other words, the manufacturer claims that 92% of the time, the test accurately determines whether or not the patient has MRSA.

A. Explain why the MRSA test results on each patient (whether or not the patient has MRSA) is considered qualitative categorical data.

B. Suppose a random sample of 30 patients is selected and each is given a MRSA test. Assuming that the test is 92% accurate, is this sample size large enough to ensure that the sampling distribution of the sample proportion (of patients for whom the test gives accurate results) is normal? Explain.

C. Assuming that the test is 92% accurate, fully describe the sampling distribution of the sample proportion (of patients for whom the test gives accurate results) for a sample of 300 patients.

D. Suppose that a random sample of 300 patients are given a MRSA test, and 268 students receive an accurate diagnosis. Assuming that the test is 92% accurate, what is the probability that 268 or fewer of these 300 patients (268/300 = 0.8933) receive an accurate MRSA diagnosis from the test?

E. (3 points Extra Credit) Does the fact that only 268 of the 300 patients in Part D receive an accurate MRSA diagnosis cause you to doubt the manufacturer’s claim (that its test has an accuracy rate of 92%)? Explain.