Chapter 11.5, Problem 14E

To determine

To calculate:

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

Answer to Problem 14E

Margin of error for a survey that has $6400$ sample size is $1.3\%$ .

Explanation of Solution

Given information:

Sample size: $6400$

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 $=6400$

Substitute the values in above formula,

  $\begin{array}{l}=\pm \frac{1}{\sqrt{n}}\\ =\pm \frac{1}{\sqrt{6400}}\\ =0.0125\\ =1.307\end{array}$

Hence, Margin of error for a survey that has $6400$ sample size is $1.3\%$ .