1. Can we use the large-sample con?dence interval? In each of the following circumstances state whether you would use the large-sample con?dence interval.
(a) n1 = 30, n2 = 30, X1 = 10, and X2 = 15.
(b) n1 = 15, n2 = 10, X1 = 10, and X2 = 5.
(c) n1 = 25, n2 = 20, X1 = 11, and X2 = 8.
(d) n1 = 40, n2 = 40, X1 = 20, and X2 = 12.
(e) n1 = 50, n2 = 50, X1 = 40, and X2 = 45.
2. More on whether to use the large-sample con?dence interval. In each of the following circumstances state whether you would use the large-sample con?dence interval.
(a) n1 = 25, n2 = 25, X1 = 12, and X2 = 8.
(b) n1 = 25, n2 = 25, X1 = 17, and X2 = 12.
(c) n1 = 60, n2 = 30, X1 = 30, and X2 = 15.
(d) n1 = 60, n2 = 55, X1 = 45, and X2 = 37.
(a) Find the mean and the standard deviation of the distribution of pˆ 1 - pˆ 2.
(b) This distribution is approximately Normal. Sketch this Normal distribution and mark the location of the mean.
(c) Find a value d for which the probability is 0.95 that the difference in sample proportions is within ±d. Mark these values on your sketch.