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 preliminary 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?