Chapter 23, Problem 11E

To determine

To explain why should you be hesitant to trust this confidence interval.

Explanation of Solution

It is given that a sample of $20$ CEOs from the Forbes $500$ shows total annual compensations ranging from a minimum of $\$0.1\text{ to \$62}\text{.24}$ million. The average for these CEOs is $\$7.946$ million. The histogram for the same is given in the question. And based on these data, a computer program found that a $95\%$ confidence interval for the mean annual compensation of all Forbes $500$ CEOs is $(1.69,14.20)$ million dollar. Thus we should be hesitant to trust this confidence interval as we cannot use the t -test because the conditions are not met. It is highly skewed right and there is an outlier.