Chapter 5.2, Problem 5.39E

To determine

To explain why the larger sample is useful and provide a backup by using a quick method to estimate the margin of error for samples.

Answer to Problem 5.39E

  $\begin{array}{l}{\text{ME}}_{25}=0.2\\ {\text{ME}}_{100}=0.1\end{array}$

Explanation of Solution

A larger sample size decreases the margin of error, making it more precise.

The margin of error is as,

  $\begin{array}{l}\text{ME=}\frac{1}{\sqrt{n}}\\ \text{Sample Size 25}\\ {\text{ME}}_{25}=\frac{1}{5}=0.2\\ \text{Sample Size 100}\\ {\text{ME}}_{100}=\frac{1}{100}=0.1\end{array}$