Question

A sample survey interviews SRSs of $500$female college students and $550$male college students. Each student is asked whether he or she worked for pay last summer. In all, 410 of the women and 484 of the men say “Yes.” The pooled sample proportion who worked last summer is about

(a) ${\stackrel{⏜}{p}}_C=1.70$

(b)${\hat{p}}_C=0.89$

(c) ${\hat{p}}_C=0.88$

(d) ${\hat{p}}_C=0.85$

(e) ${\hat{p}}_C=0.82$

Short answer

The pooled sample proportion who worked last summer is option (c)${\hat{p}}_C\approx 0.851.$

Step-by-step solution

Given information

SRS of female college students $=500$

SRS of male college students $=550$

Number of women worked summer $=410$

Number of men worked summer $=484$

Find the pooled sample proportion who worked last summer.

Explanation

The given values are taken as

$x_1=410$

$n_1=500$

$x_1=484$

$n_2=550$

The proportion of pooled sample is

localid="1650360509081" $$\begin{gathered} {\hat{p}}_C=\frac{x_1+x_2}{n_1+n_2} \\ =\frac{410+484}{500+550} \\ =\frac{894}{1050} \\ \approx 0.85 \end{gathered}$$

${\hat{p}}_C\approx 0.851.$