(b) Find the $99 \%$ confidence interval of the mean number of jobs. Round intermediate and final answers to one decimal place.
\[
6.1< \mu< 7.5
\]

Part 3 of 4
(c) Find the $95 \%$ confidence interval of the mean number of jobs. Round intermediate and final answers to one decimal place.
\[
6.3< \mu< 7.3
\]

Part: $3 / 4$

Part 4 of 4
(d) Which is smaller? Explain why.

The $\square \%$ confidence interval is smaller since there is (Choose one) $\mathbf{V}$ of a chance that the mean is contained in the interval as opposed to the $\square \%$ confidence interval.

Step 1 ：The question is asking to compare the two confidence intervals given in parts (b) and (c) and determine which one is smaller. The size of a confidence interval is determined by its range, which is the difference between the upper and lower limits of the interval. The smaller the range, the smaller the confidence interval.

Step 2 ：To find out which confidence interval is smaller, calculate the range of both intervals and compare them. The range of an interval is calculated as the upper limit minus the lower limit.

Step 3 ：The range of the 99% confidence interval is \(7.5 - 6.1 = 1.4\)

Step 4 ：The range of the 95% confidence interval is \(7.3 - 6.3 = 1.0\)

Step 5 ：So, the 95% confidence interval is smaller.

Step 6 ：The reason why the 95% confidence interval is smaller is because it is less confident. A 99% confidence interval is more confident that the true mean lies within its range, so it needs to be wider to accommodate for more possible values of the mean. On the other hand, a 95% confidence interval is less confident, so it can afford to be narrower.

Step 7 ：\(\boxed{\text{The 95% confidence interval is smaller since there is less of a chance that the mean is contained in the interval as opposed to the 99% confidence interval.}}\)