Chapter 5.2, Problem 5.52E

(a)

To determine

To explain how would the margin of error for $\text{99\%}$ confidence based on the same sample compare with the margin of error for $\text{95\%}$ confidence.

Answer to Problem 5.52E

It will increase.

Explanation of Solution

The confidence level has increased from $95\%\text{ to 99\%}$ .

As the confidence level increases, we are more confident that the true parameter is in the confidence interval. We can only become more confident, if the confidence interval contains more possible for the parameter and thus the confidence interval needs to be wider.

Since the margin of error is half the width of the confidence interval, the margin of error increases.

(b)

To determine

To explain how can we get a smaller margin of error, still with the $\text{95\%}$ confidence.

Answer to Problem 5.52E

Sample size n increases.

Explanation of Solution

The margin of error and the sample size are related by the following formula:

  $\text{ME=}\frac{1}{\sqrt{n}}$

We then note that the margin of error will decrease, when the sample size n increases.