Suppose that n items are sampled from a manufacturing process and the number of defective items found among these is X. Denote the unknown true proportion of defective items by?
(a) Consider the estimator (X + 0.5)/(n + 1) for ?. Is this estimator unbiased? Compute its mean squared error.
(b) Supppose n = 100 and the observed value of X is x = 14. Find an approximate 95% confidence interval for ?.
(c) Interpret the confidence interval found in part (b).