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

Question

asked Dec 19, 2021 108k views

1 Answer

Dglozano · Answer 1 · 2021-12-25T19:32:56+0000

Answer:

SE_p = 0.04

Step-by-step 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 = (M)/(Total)

P = (50)/(150)

P = (1)/(3)

For Women:

Q = (W)/(Total)

Q = (100)/(150)

Q = (2)/(3)

The standard error of population is calculated as thus:

$SE_p = \sqrt{(PQ)/(N)}$

$SE_p = \sqrt{((1)/(3) * (2)/(3))/(150)}$

$SE_p = \sqrt{((2)/(9))/(150)}$

$SE_p = \sqrt{(2)/(9*150)}$

$SE_p = \sqrt{(2)/(1350)$

SE_p = √(0.00148148148)

SE_p = 0.03849001792

SE_p = 0.04 Approximately