Chapter 22, Problem 1E

To determine

Find the standard error of the difference in the sample proportion.

Answer to Problem 1E

The standard error of the difference in the sample is 0.01614.

Explanation of Solution

Given info:

In one survey it was seen that 192 of 960 Canadians born in another country. Similarly 170 out of 1250 U.S. citizen born in foreign country.

Calculation:

Let ${\widehat{p}}_{Can}$ is the proportion of Canadians, who born in another country and ${\widehat{p}}_{Am}$ is the proportion of Americans, who born in another country.

Point estimates:

$\begin{array}{c}{\widehat{p}}_{Can}=\frac{192}{960}\\ =0.2\end{array}$

$\begin{array}{c}{\widehat{p}}_{Am}=\frac{170}{1,250}\\ =0.136\end{array}$

The standard error of the difference is,

$\begin{array}{c}SE\left({\widehat{p}}_{Can}-{\widehat{p}}_{Am}\right)=\sqrt{\frac{{\widehat{p}}_{Can}{\widehat{q}}_{Can}}{n_{Can}}+\frac{{\widehat{p}}_{Am}{\widehat{q}}_{Am}}{n_{Am}}}\\ =\sqrt{\frac{0.2\times 0.8}{960}+\frac{0.136\times 0.864}{1,250}}\\ =\sqrt{0.000261}\\ =0.01614\end{array}$

Hence, the standard error is 0.01614.