Question

A sample of 150 U.S. adults is composed of 100 women and 50 men. Estimate the standard error of the proportions for the female population.

.04

127.17

.001

1.26

Answer 1

Answer:

$SE_p = 0.04$

Explanation:

Given

Represent Women with W and Men with M

$M = 50$

$W = 100$

$Total = 150$

Required

Determine the standard error of the female population

First, we need to determine the proportion of both gender.

For Men:

$P = \frac{M}{Total}$

$P = \frac{50}{150}$

$P = \frac{1}{3}$

For Women:

$Q = \frac{W}{Total}$

$Q = \frac{100}{150}$

$Q = \frac{2}{3}$

The standard error of population is calculated as thus:

$SE_p = \sqrt{\frac{PQ}{N}}$

$SE_p = \sqrt{\frac{\frac{1}{3} * \frac{2}{3}}{150}}$

$SE_p = \sqrt{\frac{\frac{2}{9}}{150}}$

$SE_p = \sqrt{\frac{2}{9*150}}$

$SE_p = \sqrt{\frac{2}{1350}$

$SE_p = \sqrt{0.00148148148}$

$SE_p = 0.03849001792$

$SE_p = 0.04$ Approximately