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

`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