Chapter 11.5, Problem 19E

To determine

To calculate:

Number of sample size and correct the error.

Answer to Problem 19E

Sample size is $625$ and Error observed as the wrong percentage was substituted in the given equation.

Explanation of Solution

Given information:

Margin of error: $\pm 4\%$

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, It is given that,

  $\begin{array}{l}\pm 0.08=\pm \frac{1}{\sqrt{n}}\\ 0.0064=\frac{1}{n}\\ n=156\end{array}$

But by using given margin of error $\pm 4\%$ calculations forsample size is,

  $\begin{array}{l}\pm 0.04=\pm \frac{1}{\sqrt{n}}\\ \pm 0.0016=\frac{1}{n}\\ n=625\end{array}$

Hence, sample size is $625$ .

Error observed as the wrong percentage was substituted in the given equation.