Chapter 11.5, Problem 12E

To determine

To calculate:

Margin of error for a survey that has given sample size.

Answer to Problem 12E

Margin of error for a survey that has $1000$ sample size is $3.2\%$ .

Explanation of Solution

Given information:

Sample size: $1000$

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 sample size $=1000$

Substitute the values in above formula,

  $\begin{array}{l}=\pm \frac{1}{\sqrt{n}}\\ =\pm \frac{1}{\sqrt{1000}}\\ =0.03162\\ =\pm 3.162\end{array}$

Hence, Margin of error for a survey that has $1000$ sample size is $3.2\%$ .