Question: Suppose a clinical trial is conducted to test the efficacy of a new drug, spectinomycin, in the treatment of gonorrhea for females. Forty-six patients are given a 4 grams daily dose of the drug and seen one week later, at which time six of the patients still have gonorrhea.

a) What is the best point estimate of p, the probability of a failure with the drug? What is the standard error of the estimate?

b) What is a 95% confidence interval for p?

c) Suppose we know that penicillin G at a daily dose of 4.8 mega-units has 10% failure rate. Conduct the appropriate test to determine if the rate of failure for spectinomycin differs from 10%.

d) What role does the central limit theorem play in this problem?