A study was recently conducted at a major university to estimate the difference in the proportion of business school and non-business school graduates who go on to a higher degree programme within five years of graduation A random sample of 400 business school graduates showed that 75 had gone to graduate school, while in a random sample of 500 non-business graduates, 137 had done so. The 95% confidence interval is
A) -0.1412 to -0.0318
B) -2.0465 to 1.8375
C) -0.0880 to -0.0850
D) -0.1144 to -0.0586
E) -0.0873 to -0.0857

Question

Quizplus · Accepted Answer

The 95% confidence interval for the difference in proportions is:p1 - p2 +/- 1.96 * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))where p1 is the proportion of business school graduates who go on to a higher degree programme, p2 is the proportion of non-business school graduates who go on to a higher degree programme, n1 is the sample size of business school graduates, and n2 is the sample size of non-business school graduates.Plugging in the values we get:0.75 - 0.137 +/- 1.96 * sqrt((0.75 * (1 - 0.75) / 400) + (0.137 * (1 - 0.137) / 500))= 0.613 +/- 0.055= (0.558, 0.668)Therefore, the 95% confidence interval is -0.1412 to -0.0318.

A Study Was Recently Conducted at a Major University to Estimate