Question

In a recent Pew Research poll, 287 out of 522 randomly selected men in the U.S. were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected women were asked, 233 were able to do so. Construct a 95% confidence interval for the difference in the proportion of U.S. men and the proportion of U.S. women who can identify Egypt on a map.

Answer 1

n1 = 522 and n2 = 520

Here, sample proportion for men , 1 = (287/522)

= 0.549

Here, sample proportion for women , 2 = (233/520)

= 0.448

Now, the z value for 95% confidence level = 1.96

The confidence interval is = (1 - 2) z* {1 (1- 1 ) / n1 + 2 (1- 2 ) / n2}

= 0.101   1.96 * 0.0308

= 0.101   0.0604

=(0.0406 , 0.1614)