Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed. c= 0.95, x= 13.1, s= 3.0, n 8 ..... (Round to one decimal place as needed.)
Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed. c= 0.95, x= 13.1, s= 3.0, n 8 ..... (Round to one decimal place as needed.)
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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![**Constructing a Confidence Interval for the Population Mean**
To construct the indicated confidence interval for the population mean (\(\mu\)) using the t-distribution, we will assume the population is normally distributed. The given values are:
- Confidence level (\(c\)) = 0.95
- Sample mean (\(\bar{x}\)) = 13.1
- Sample standard deviation (\(s\)) = 3.0
- Sample size (\(n\)) = 8
**Instructions:**
Calculate the confidence interval using the formula for the t-distribution. The steps involved are:
1. Determine the degrees of freedom (\(df\)) as \(n - 1\).
2. Use the t-distribution table to find the t-score corresponding to the confidence level and the calculated degrees of freedom.
3. Calculate the margin of error as:
\[
\text{Margin of Error} = t \times \left(\frac{s}{\sqrt{n}}\right)
\]
4. Determine the confidence interval using the formula:
\[
\text{Confidence Interval} = \bar{x} \pm \text{Margin of Error}
\]
5. Round your final answer to one decimal place.
This process will help you estimate the range in which the true population mean is likely to fall with a specified level of confidence (95% in this case).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7a24eb4-57b8-4308-8ec2-e6ee4c7ba268%2F1ccc7030-8da5-4da5-8c15-a31374c49b44%2F1r3qgp9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Constructing a Confidence Interval for the Population Mean**
To construct the indicated confidence interval for the population mean (\(\mu\)) using the t-distribution, we will assume the population is normally distributed. The given values are:
- Confidence level (\(c\)) = 0.95
- Sample mean (\(\bar{x}\)) = 13.1
- Sample standard deviation (\(s\)) = 3.0
- Sample size (\(n\)) = 8
**Instructions:**
Calculate the confidence interval using the formula for the t-distribution. The steps involved are:
1. Determine the degrees of freedom (\(df\)) as \(n - 1\).
2. Use the t-distribution table to find the t-score corresponding to the confidence level and the calculated degrees of freedom.
3. Calculate the margin of error as:
\[
\text{Margin of Error} = t \times \left(\frac{s}{\sqrt{n}}\right)
\]
4. Determine the confidence interval using the formula:
\[
\text{Confidence Interval} = \bar{x} \pm \text{Margin of Error}
\]
5. Round your final answer to one decimal place.
This process will help you estimate the range in which the true population mean is likely to fall with a specified level of confidence (95% in this case).
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