Chapter 12.2, Problem 22PPS

a)

To determine

To find : What is the margin of sampling error ?

Answer to Problem 22PPS

  $\pm 0.01540$

Explanation of Solution

Given Information :

  $78\%$ people exercise, in a survey of $4213$ people, at least one hour each week.

Formula Used:

Margin of sampling error = $\pm \frac{1}{\sqrt{n}}$ .

Calculation :

Sampling error margin = $\pm \frac{1}{\sqrt{4213}}=\pm 0.01540$

b)

To determine

To find : What is the likely interval that contains the percentage of the population that do at least once hour of exercise each week ?

Answer to Problem 22PPS

Interval between $76.46\%$ and $79.54\%$

Explanation of Solution

Given Information :

A survey of $4213$ people, $78\%$ exercise at least one hour each week.

Calculation :

  $78\%\pm$ sampling error margin.

  $\begin{array}{l}\Rightarrow 78\%\pm (0.0154\times 100)\%\\ \Rightarrow 78\%\pm 1.54\end{array}$

  $\Rightarrow$ interval between $76.46\%$ and $79.54\%$ .