Homework 7.1 Question 2 of 3 (3 points) | Question Attempt: 1 of 5 Part 1 of 4 (a) The best point estimate of the mean is \( \square \) 29 pounds. Part 2 of 4 (b) Find the \( 95 \% \) confidence interval of the mean of these pounds. Round intermediate answers to at least three decimal places. Round your final answ to one decimal place. \[ 28.0<\mu<30.0 \] Part 3 of 4 (c) Find the \( 99 \% \) confidence interval of the mean of these pounds. Round intermediate answers to at least three decimal places. Round your final answe to one decimal place. \[ 27.7<\mu<30.3 \] Part: 3 / 4 Part 4 of 4 (d) Which interval is larger? Why? The \( 95 \% \) confidence interval is larger. An interval with a \( \square \) greater range of values than the 90 \% confidence interval will be more likely to contain the true population mean. Try again ip Part Recheck Save For Later Sub AcGraw Hill LLC. All Rights Reserved. Terms of Use Privacy

**Step 1.** We are given: - The best point estimate of the mean is \(29\) pounds. **Step 2.** The \(95\%\) confidence interval is given as: \[ 28.0 < \mu < 30.0 \] which has a width of: \[ 30.0 - 28.0 = 2.0 \text{ pounds}. \] **Step 3.** The \(99\%\) confidence interval is given as: \[ 27.7 < \mu < 30.3 \] which has a width of: \[ 30.3 - 27.7 = 2.6 \text{ pounds}. \] **Step 4.** To determine which interval is larger, we compare the widths of the intervals. The \(99\%\) confidence interval has a width of \(2.6\) pounds, while the \(95\%\) confidence interval has a width of \(2.0\) pounds. Therefore, the \(99\%\) confidence interval is larger. **Step 5.** The reason for this is that a higher confidence level (in this case, \(99\%\)) requires a wider interval in order to be more certain that the true population mean is captured. A higher level of confidence means you are less likely to miss the true mean, which is achieved by increasing the margin of error. Thus, the \(99\%\) confidence interval is larger because it has a greater margin of error owing to the higher confidence requirement.