A candy manufacturer selects mints at random from the production line and weighs them. For one week, the day shift weighed n1 = 194 mints and the night shift weighed n2 = 162 mints. The numbers of these mints that weighed at most 21 grams was y1 = 28 for the day shift and y2 = 11 for the night shift. Let p1 and p2 denote the proportions of mints that weigh at most 21 grams for the day and night shifts, respectively.
(a) Give a point estimate of p1.
(b) Give the endpoints for a 95% confidence interval for p1.
(c) Give a point estimate of p1 − p2.
(d) Find a one-sided 95% confidence interval that gives a lower bound for p1 − p2.