A central Pennsylvania attorney reported that the Northumberland County district attorney’s (DA) office trial record showed only 6 convictions in 27 trials from January to mid-July 1997. Four central Pennsylvania county DAs responded, “Don’t judge us by statistics!”18

a. If the attorney’s information is correct, would you reject a claim by the DA of a 50% or greater conviction rate?

b. The actual records show that there have been 455 guilty pleas and 48 cases that have gone to trial. Even assuming that the 455 guilty pleas are the only convictions of the 503 cases reported, what is the 95% confidence interval for p, the true proportion of convictions by this district attorney?

c. Using the results of part b, are you willing to reject a figure of 50% or greater for the true conviction rate? Explain.