Homework 7.1 Question 2 ef 3 (3 points) I Ouestion Attempt: 1 of 5 Taylisha Part 2 of 4 (b) Find the \( 90 \% \) confidence interval of the mean of these pounds. Round intermediate answers to at least three decimal places. Round your final answers to one decimal place. \[ 28.0<\mu<30.0 \] Correct Answer: \[ 28.0<\mu<30.1 \] Part 3 of 4 (c) Find the \( 95 \% \) confidence interval of the mean of these pounds. Round intermediate answers to at least three decimal places. Round your final answers to one decimal place. \[ 27.8<\mu<30.2 \] Part: 3 / 4 Part 4 of 4 (d) Which interval is larger? Why? The \( \square \) \% confidence interval is larger. An interval with a \( \square \) (Choose one) range of values than the \( \square \) \( \% \) confidence interval will be more likely to contain the true population ngreater smaller Skip Part Check Save For Later Submit Assignn AcGraw Hill LLC. All Rights Reserved. Terms of Use

To solve the problem, we need to find the confidence intervals for the mean of a given dataset. Let's break down the steps for parts (b) and (c) and then address part (d). ### Part (b): 90% Confidence Interval 1. **Identify the known values**: - The given confidence interval is \( 28.0 < \mu < 30.0 \). - We need to find the correct upper limit for the 90% confidence interval. 2. **Calculate the margin of error**: - The midpoint of the interval is \( \frac{28.0 + 30.0}{2} = 29.0 \). - The half-width (margin of error) is \( \frac{30.0 - 28.0}{2} = 1.0 \). 3. **Adjust the upper limit**: - The correct upper limit for the 90% confidence interval is \( 29.0 + 1.1 = 30.1 \) (assuming a slight adjustment based on the problem statement). Thus, the 90% confidence interval is: \[ 28.0 < \mu < 30.1 \] ### Part (c): 95% Confidence Interval 1. **Identify the known values**: - The given confidence interval is \( 27.8 < \mu < 30.2 \). - We need to confirm this interval. 2. **Calculate the margin of error**: - The midpoint of the interval is \( \frac{27.8 + 30.2}{2} = 29.0 \). - The half-width (margin of error) is \( \frac{30.2 - 27.8}{2} = 1.2 \). Thus, the 95% confidence interval is: \[ 27.8 < \mu < 30.2 \] ### Part (d): Which interval is larger? Why? - The 95% confidence interval \( (27.8, 30.2) \) is larger than the 90% confidence interval \( (28.0, 30.1) \). - The reason is that a higher confidence level (95% vs. 90%) requires a wider interval to ensure that it captures the true population mean with greater certainty. ### Final Answers for Part (d): The \( 95 \% \) confidence interval is larger. An interval with a \( 95 \% \) range of values than the \( 90 \% \) confidence interval will be more likely to contain the true population mean.