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Comparing the 3 confidence intervals above Questions 2, 3 and 4 (90%, 95% and 99%): • Provide a conclusion that can be made based on each confidence interval. • Which has the largest margin of error? • Which confidence interval provides us with the highest certainty of accuracy? • If we increased the sample size (n), would the margin of error increase or decrease? Edit View Insert Format Tools Table 12pt Paragraph | BI U AV T² : Question 2: 28.4

Comparing the 3 confidence intervals above Questions 2, 3 and 4 (90%, 95% and 99%): • Provide a conclusion that can be made based on each confidence interval. • Which has the largest margin of error? • Which confidence interval provides us with the highest certainty of accuracy? • If we increased the sample size (n), would the margin of error increase or decrease? Edit View Insert Format Tools Table 12pt Paragraph | BI U AV T² : Question 2: 28.4

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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# Comparing Confidence Intervals When analyzing data, it's crucial to understand the concept of confidence intervals. Confidence intervals give us a range within which we can expect the true population parameter (like a mean or proportion) to fall. Here, we'll compare three confidence intervals at different confidence levels: 90%, 95%, and 99%. ### Confidence Intervals from Questions 2, 3, and 4 1. **Question 2:** - Confidence Interval: \( 28.4 < u < 30.6 \) - Confidence Level: 90% 2. **Question 3:** - Confidence Interval: \( 28.1 < u < 30.9 \) - Confidence Level: 95% 3. **Question 4:** - Confidence Interval: \( 27.7 < u < 31.3 \) - Confidence Level: 99% ### Analysis and Questions **1. Provide a conclusion that can be made based on each confidence interval.** Each confidence interval gives us a different range for where we believe the true population parameter lies. With higher confidence levels, the interval becomes wider. This reflects increased confidence that the interval contains the true population parameter. - For Question 2, we are 90% confident the true value falls between 28.4 and 30.6. - For Question 3, we are 95% confident the true value falls between 28.1 and 30.9. - For Question 4, we are 99% confident the true value falls between 27.7 and 31.3. **2. Which has the largest margin of error?** The margin of error is half the width of the confidence interval. The interval with the highest confidence level (99%) generally has the largest margin of error because it needs to cover a larger range to ensure higher confidence. Using this information: - For Question 2 (90%), margin of error = \((30.6 - 28.4) / 2 = 1.1\) - For Question 3 (95%), margin of error = \((30.9 - 28.1) / 2 = 1.4\) - For Question 4 (99%), margin of error = \((31.3 - 27.7) / 2 = 1.8\) Question 4 has the largest margin of error.
Transcribed Image Text:# Comparing Confidence Intervals When analyzing data, it's crucial to understand the concept of confidence intervals. Confidence intervals give us a range within which we can expect the true population parameter (like a mean or proportion) to fall. Here, we'll compare three confidence intervals at different confidence levels: 90%, 95%, and 99%. ### Confidence Intervals from Questions 2, 3, and 4 1. **Question 2:** - Confidence Interval: \( 28.4 < u < 30.6 \) - Confidence Level: 90% 2. **Question 3:** - Confidence Interval: \( 28.1 < u < 30.9 \) - Confidence Level: 95% 3. **Question 4:** - Confidence Interval: \( 27.7 < u < 31.3 \) - Confidence Level: 99% ### Analysis and Questions **1. Provide a conclusion that can be made based on each confidence interval.** Each confidence interval gives us a different range for where we believe the true population parameter lies. With higher confidence levels, the interval becomes wider. This reflects increased confidence that the interval contains the true population parameter. - For Question 2, we are 90% confident the true value falls between 28.4 and 30.6. - For Question 3, we are 95% confident the true value falls between 28.1 and 30.9. - For Question 4, we are 99% confident the true value falls between 27.7 and 31.3. **2. Which has the largest margin of error?** The margin of error is half the width of the confidence interval. The interval with the highest confidence level (99%) generally has the largest margin of error because it needs to cover a larger range to ensure higher confidence. Using this information: - For Question 2 (90%), margin of error = \((30.6 - 28.4) / 2 = 1.1\) - For Question 3 (95%), margin of error = \((30.9 - 28.1) / 2 = 1.4\) - For Question 4 (99%), margin of error = \((31.3 - 27.7) / 2 = 1.8\) Question 4 has the largest margin of error.
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