Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed. c=0.95, x= 14.3, s= 0.74, n=13 (00 (Round to one decimal place as needed.)
Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed. c=0.95, x= 14.3, s= 0.74, n=13 (00 (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 Using the t-distribution**
In this exercise, you will construct the indicated confidence interval for the population mean (μ) using the t-distribution. Assume that the population is normally distributed with the following statistics provided:
- Confidence level (c): 0.95
- Sample mean (\(\bar{x}\)): 14.3
- Sample standard deviation (s): 0.74
- Sample size (n): 13
_**Steps to construct the confidence interval:**_
1. **Calculate the degrees of freedom (df):**
\[ df = n - 1 \]
2. **Find the t-critical value (t\(_{\alpha/2}\)) for the given confidence level and degrees of freedom.**
You can find this value in a t-distribution table or using a calculator.
3. **Compute the margin of error (ME):**
\[ ME = t\(_{\alpha/2}\) \times \left( \frac{s}{\sqrt{n}} \right) \]
4. **Determine the confidence interval:**
\[ \left( \bar{x} - ME, \bar{x} + ME \right) \]
_**Visual Aid (Explanation of Diagram):**_
In the image, there is a placeholder for the confidence interval with empty brackets, indicating where the computed interval should be filled in. The instruction below asks to round the final values to one decimal place as needed.
**Placeholder for Confidence Interval:**
\[ (\_\_ , \_\_) \]
(Round to one decimal place as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe21ad11-6e18-4b63-a679-8109648f0f0b%2F59a0b7b6-9fb2-4159-94b6-be6f0f54057d%2F9n1rxmg_processed.png&w=3840&q=75)
Transcribed Image Text:**Constructing a Confidence Interval for the Population Mean Using the t-distribution**
In this exercise, you will construct the indicated confidence interval for the population mean (μ) using the t-distribution. Assume that the population is normally distributed with the following statistics provided:
- Confidence level (c): 0.95
- Sample mean (\(\bar{x}\)): 14.3
- Sample standard deviation (s): 0.74
- Sample size (n): 13
_**Steps to construct the confidence interval:**_
1. **Calculate the degrees of freedom (df):**
\[ df = n - 1 \]
2. **Find the t-critical value (t\(_{\alpha/2}\)) for the given confidence level and degrees of freedom.**
You can find this value in a t-distribution table or using a calculator.
3. **Compute the margin of error (ME):**
\[ ME = t\(_{\alpha/2}\) \times \left( \frac{s}{\sqrt{n}} \right) \]
4. **Determine the confidence interval:**
\[ \left( \bar{x} - ME, \bar{x} + ME \right) \]
_**Visual Aid (Explanation of Diagram):**_
In the image, there is a placeholder for the confidence interval with empty brackets, indicating where the computed interval should be filled in. The instruction below asks to round the final values to one decimal place as needed.
**Placeholder for Confidence Interval:**
\[ (\_\_ , \_\_) \]
(Round to one decimal place as needed.)
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