Chapter 11.6, Problem 21HP

To determine

To find: The sample size for the given interval.

Answer to Problem 21HP

The sample size for the given intervalis $44$ .

Explanation of Solution

Given Information:

The mean weight of a box is $20\text{ounce}$ and the sample standard deviation is $0.128\text{ounce}$ .

Obtain the z- value from the z-table of $95\%$ confidence corresponding to the given mean and standard deviation is $1.96$ .

The maximum error of the estimateis calculated as,

  $\begin{array}{c}E=\frac{20.008-19.932}{2}\\ =0.038\end{array}$

The sample size for the given interval is calculated as,

  $\begin{array}{l}E=z\times \frac{s}{\sqrt{n}}\\ 0.038=\left(1.96\right)\left(\frac{0.128}{\sqrt{n}}\right)\\ n\approx 44\end{array}$

Hence, the sample size for the given intervalis $44$ .