In a random sample of 24 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct a 80% confidence interval for the population mean μ. What is the margin of error of µ? Interpret the results. The confidence interval for the population mean u is (Round to one decimal place as needed.) The margin of error of μ is. (Round to one decimal place as needed.) Interpret the results. OA. If a large sample of people are taken approximately 80% of them will have commute times between the bounds of the confidence interval. OB. With 80% confidence, it can be said that the commute time is between the bounds of the confidence interval. OC. It can be said that 80% of people have a commute time between the bounds of the confidence interval. O D. With 80% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.
In a random sample of 24 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct a 80% confidence interval for the population mean μ. What is the margin of error of µ? Interpret the results. The confidence interval for the population mean u is (Round to one decimal place as needed.) The margin of error of μ is. (Round to one decimal place as needed.) Interpret the results. OA. If a large sample of people are taken approximately 80% of them will have commute times between the bounds of the confidence interval. OB. With 80% confidence, it can be said that the commute time is between the bounds of the confidence interval. OC. It can be said that 80% of people have a commute time between the bounds of the confidence interval. O D. With 80% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.
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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![**Sample Problem Statement:**
In a random sample of 24 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct an 80% confidence interval for the population mean μ. What is the margin of error of μ? Interpret the results.
---
**Solution:**
**1. Construct the Confidence Interval:**
The confidence interval for the population mean μ is ( ___ , ___ ).
(Round to one decimal place as needed).
**2. Calculate the Margin of Error:**
The margin of error of μ is ___.
(Round to one decimal place as needed).
---
**Interpretation of Results:**
Select the correct interpretation:
A. O If a large sample of people are taken approximately 80% of them will have commute times between the bounds of the confidence interval.
B. O With 80% confidence, it can be said that the commute time is between the bounds of the confidence interval.
C. O It can be said that 80% of people have a commute time between the bounds of the confidence interval.
D. O With 80% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.
---
**Explanation:**
To solve this problem, follow these steps:
1. **Identify the sample statistics:**
- Mean (\(\bar{x}\)) = 31.2 minutes
- Standard deviation (s) = 7.1 minutes
- Sample size (n) = 24
2. **Determine the t-score for the 80% confidence level:**
- Degrees of freedom (df) = n - 1 = 24 - 1 = 23
- Use a t-distribution table or calculator to find the t-score for 80% confidence with 23 degrees of freedom.
3. **Calculate the Margin of Error (E):**
\[
E = t \times \left(\frac{s}{\sqrt{n}}\right)
\]
4. **Construct the Confidence Interval:**
\[
\text{CI} = \bar{x} \pm E
\]
Remember to round the final answers to one decimal place as instructed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15e40907-5866-4802-8bee-6781a38984f9%2F55c5b9ff-4ab8-49db-9ec7-42ef00734702%2F96eq34_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Sample Problem Statement:**
In a random sample of 24 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct an 80% confidence interval for the population mean μ. What is the margin of error of μ? Interpret the results.
---
**Solution:**
**1. Construct the Confidence Interval:**
The confidence interval for the population mean μ is ( ___ , ___ ).
(Round to one decimal place as needed).
**2. Calculate the Margin of Error:**
The margin of error of μ is ___.
(Round to one decimal place as needed).
---
**Interpretation of Results:**
Select the correct interpretation:
A. O If a large sample of people are taken approximately 80% of them will have commute times between the bounds of the confidence interval.
B. O With 80% confidence, it can be said that the commute time is between the bounds of the confidence interval.
C. O It can be said that 80% of people have a commute time between the bounds of the confidence interval.
D. O With 80% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.
---
**Explanation:**
To solve this problem, follow these steps:
1. **Identify the sample statistics:**
- Mean (\(\bar{x}\)) = 31.2 minutes
- Standard deviation (s) = 7.1 minutes
- Sample size (n) = 24
2. **Determine the t-score for the 80% confidence level:**
- Degrees of freedom (df) = n - 1 = 24 - 1 = 23
- Use a t-distribution table or calculator to find the t-score for 80% confidence with 23 degrees of freedom.
3. **Calculate the Margin of Error (E):**
\[
E = t \times \left(\frac{s}{\sqrt{n}}\right)
\]
4. **Construct the Confidence Interval:**
\[
\text{CI} = \bar{x} \pm E
\]
Remember to round the final answers to one decimal place as instructed.
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