Question

About 80% of MCC students believe they can achieve the American dream and about 63% of Ferris State Universtiy students believe they can achieve the American dream. Construct a 95% confidence interval for the difference in the proportions of Montcalm Community College students and Ferris State University students who believe they can achieve the American dream. There were 100 MCC students surveyed and 100 FSU students surveyed. a. With 95% confidence the difference in the proportions of MCC and FSU students who believe they can achieve the American dream is (round to 3 decimal places) and (round to 3 decimal places). b. If many groups of 100 randomly selected MCC students and 100 randomly selected FSU students were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of the difference in the proportions of MCC students and FSU students who believe they can achieve the American dream about percent will not contain the true population difference in proportions.

Answer 1

Let p1,P2 denote the respective sample proportions and n1, n2 denotes the sample sizes respectively. Here, Pi = 0.800, n1 = 100, p2 = 0.630, n2 = 100 Standard error of sampling distribution of difference in sample proportions is Pi * (1 – p1) , P2 * (1 – p2) 0.80 * (1 – 0.80) 0.63 * (1 – 0.63) SE = = 0.062698 100 100 n1 n2 Margin of error is Pi * (1 – pi) , P2 * (1 – p2) 0.80 * (1 – 0.80) 0.63 * (1 – 0.63) 0.63 * (1 – 0.63) 0.80 * (1 – 0.80) ME * 1.644854 = 0.103129 * Z1-0.95 * 20.025 100 100 100 100 n1 n2 a 95 percent confidence interval for the difference between two population proportions (p1 – P2) is p2 * (1– p2) Pi * (1 – P1) = (pi – P2) ± 2 1-0.9% * n1 n2 2 (1 – 0.63) 0.80 * (1 – 0.80) 0.63 * = (0.80 – 0.63)±%0.025 * 100 100 0.80 * (1 – 0.80) 0.63 * (1 – 0.63) = 0.17 + 1.959964 * 100 100 - 0.17 +0.103129 = (0.066871, 0.273129) (0.067,0.273)

b) 95, 5