Chapter 11.5, Problem 23E

To determine

To calculate:

Number of residents will survey.

Answer to Problem 23E

Number of residents $\left(n\right)$ will survey is $453$ .

Explanation of Solution

Given information:

Percentage: $52.3\%$ and $61.7\%$

Calculation:

In order to find the margin of error formula used is,

  $z.\sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}$

Where,

  $z=$$z-$ Score.

  $\widehat{p}=$ Sample proportion.

  $n=$ sample size.

Here given is Percentage: $52.3\%$ and $61.7\%$

So the difference is $61.7\%-52.3=9.4\%$

So for the margin of error $4.7\%$

Substitute the values in above formula,

  $\begin{array}{l}4.7=\pm \frac{1}{\sqrt{n}}\\ 4.7=\pm \frac{1}{\sqrt{n}}\\ 22.09=\frac{1}{n}\\ n=0.04526\\ n=453\end{array}$

Hence, Number of residents $\left(n\right)$ will survey is $453$ .