In medical investigations, the ratio
p1/p2 is often of more interest than the difference p1  p2 (e.g., individuals given treatment 1 are how many times as likely to recover as those given treatment 2?). Let ˆ
pˆ1/pˆ2. When m and n are both large, the statistic ln( ˆ) has approximately a normal distribution with approximate mean value ln( ) and approximate standard deviation [(m  x)/(mx) (n  y)/(ny)]1/2.

a. Use these facts to obtain a large-sample 95% CI formula for estimating ln( ), and then a CI for itself.

b. Return to the heart attack data of Example 1.3, and calculate an interval of plausible values for at the 95%

confidence level. What does this interval suggest about the efficacy of the aspirin treatment?