Question

In a Pew Research Poll, 287 out of 522 randomly selected US men were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected US women were asked, 233 were able to do so. Construct a 98% confidence interval for the true proportion of US men and US women (m-w) who can identify Egypt on a map.

answer choices
(0.0384, 0.1650)
(0.0301, 0.1733)
(0.0413, 0.1621)
(0.0510, 0.1524)

Answer 1

(0.0301, 0.1733)

Explanation:

`\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\\\CI_(98\%)=\biggr((287)/(522)-(233)/(520)\biggr)\pm 2.326\sqrt{((287)/(522)(1-(287)/(522)))/(522)+((233)/(520)(1-(233)/(520)))/(520)}\\\\\\CI_(98\%)\approx\{0.0300,0.1734\}`

Hence, the best choice is (0.0301, 0.1733) which tells us that we are 98% confident that the difference between the two proportions of men and women who successfully found Egypt on the map when highlighted is between 0.0301 and 0.1733