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distributed and use a t-distribution to construct a 98% confidence interval for the population mean µ. What is the margin of error of µ? Interpret the results.

distributed and use a t-distribution to construct a 98% confidence interval for the population mean µ. What is the margin of error of µ? Interpret the results.

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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Also need margin of error. 

**Transcription for Educational Website** --- **Title: Confidence Interval and Margin of Error Calculation** In a random sample of 29 people, the mean commute time to work was 34.5 minutes, and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean \( \mu \). What is the margin of error of \( \mu \)? Interpret the results. **The confidence interval for the population mean \( \mu \) is \((\_\_\_, \_\_\_)\).** (Round to one decimal place as needed.) --- In this scenario, we are tasked with finding a confidence interval for the average commute time using a sample mean, sample standard deviation, and a specified confidence level. The confidence interval will give us a range within which we can be 98% confident that the true population mean lies. To calculate the margin of error and the confidence interval, we typically follow these steps: 1. **Determine the sample mean (\(\bar{x}\)) and standard deviation (s):** - Sample mean (\(\bar{x}\)) = 34.5 minutes - Standard deviation (s) = 7.2 minutes 2. **Identify the sample size (n):** - Sample size (n) = 29 3. **Find the t-value for a 98% confidence level using a t-distribution table.** The degrees of freedom (df) would be \( n - 1 = 28 \). 4. **Calculate the margin of error (ME):** - Formula: \( ME = t \times \frac{s}{\sqrt{n}} \) 5. **Determine the confidence interval using the formula:** - Confidence interval = \( \bar{x} \pm ME \) Interpret the results: This will show the interval in which the true mean commute time for the population is likely to lie with 98% confidence.
Transcribed Image Text:**Transcription for Educational Website** --- **Title: Confidence Interval and Margin of Error Calculation** In a random sample of 29 people, the mean commute time to work was 34.5 minutes, and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean \( \mu \). What is the margin of error of \( \mu \)? Interpret the results. **The confidence interval for the population mean \( \mu \) is \((\_\_\_, \_\_\_)\).** (Round to one decimal place as needed.) --- In this scenario, we are tasked with finding a confidence interval for the average commute time using a sample mean, sample standard deviation, and a specified confidence level. The confidence interval will give us a range within which we can be 98% confident that the true population mean lies. To calculate the margin of error and the confidence interval, we typically follow these steps: 1. **Determine the sample mean (\(\bar{x}\)) and standard deviation (s):** - Sample mean (\(\bar{x}\)) = 34.5 minutes - Standard deviation (s) = 7.2 minutes 2. **Identify the sample size (n):** - Sample size (n) = 29 3. **Find the t-value for a 98% confidence level using a t-distribution table.** The degrees of freedom (df) would be \( n - 1 = 28 \). 4. **Calculate the margin of error (ME):** - Formula: \( ME = t \times \frac{s}{\sqrt{n}} \) 5. **Determine the confidence interval using the formula:** - Confidence interval = \( \bar{x} \pm ME \) Interpret the results: This will show the interval in which the true mean commute time for the population is likely to lie with 98% confidence.
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