An article in the Journal of the American Statistical Association (1990, Vol. 85, pp. 972-985) measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats.

(a) Calculate a 95% two-sided confidence interval on the true proportion of rats that would show underweight from the experiment. (,)

(b) Using the point estimate of p obtained from the observed sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02?

(c) How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p?