Suppose that n items are sampled from a manufacturing process and the number of de- fective items found among these is X. Denote the unknown true proportion of defective items by . If exceeds 5 percent, the line must be shut down and adjusted.
(a) Consider the estimator X/(n+1) for . Is this estimator unbiased? Compute its mean squared error.
(b) Supppose n = 200 and the observed value of X is x = 17. Find an approximate 95% confidence interval for.
(c) Interpret the confidence interval found in part (b).
(d) Set up the null and alternative hypotheses needed to detect a situation in which the proportion of defectives exceeds 0.05.