Construct the indicated confidence interval for the population meanu using the t-distribution. Assume the population is normally distributed. c= 0.90, x= 13.9, s=0.73, n= 19 .... (Round to one decimal place as needed.) Help me solve this View an example Get more help - P O Type here to search
Construct the indicated confidence interval for the population meanu using the t-distribution. Assume the population is normally distributed. c= 0.90, x= 13.9, s=0.73, n= 19 .... (Round to one decimal place as needed.) Help me solve this View an example Get more help - P O Type here to search
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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Question
![**Constructing a Confidence Interval for the Population Mean**
To construct a confidence interval for the population mean \(\mu\) using the t-distribution, follow these steps. Assume the population is normally distributed.
**Given:**
- Confidence level (\(c\)): 0.90
- Sample mean (\(\bar{x}\)): 13.9
- Sample standard deviation (\(s\)): 0.73
- Sample size (\(n\)): 19
**Goal:**
- Calculate the confidence interval.
**Instructions:**
1. **Identify the critical value** for the t-distribution using the confidence level and degrees of freedom (\(df = n - 1 = 18\)).
2. **Calculate the standard error** of the mean:
\[
SE = \frac{s}{\sqrt{n}}
\]
3. **Construct the confidence interval**:
\[
\bar{x} \pm (t \times SE)
\]
**Note:** Round the final answers to one decimal place as needed.
**Additional Resources:**
- Use the options "Help me solve this," "View an example," or "Get more help" for guided instruction and further understanding.
**Technical Note:**
Ensure your device's temperature remains optimal to facilitate smooth calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa19f5a27-b6ae-4a27-9581-cd55b4c96944%2Fc17e2ca9-317f-4416-913a-76e9dc67a802%2F3z14h9j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Constructing a Confidence Interval for the Population Mean**
To construct a confidence interval for the population mean \(\mu\) using the t-distribution, follow these steps. Assume the population is normally distributed.
**Given:**
- Confidence level (\(c\)): 0.90
- Sample mean (\(\bar{x}\)): 13.9
- Sample standard deviation (\(s\)): 0.73
- Sample size (\(n\)): 19
**Goal:**
- Calculate the confidence interval.
**Instructions:**
1. **Identify the critical value** for the t-distribution using the confidence level and degrees of freedom (\(df = n - 1 = 18\)).
2. **Calculate the standard error** of the mean:
\[
SE = \frac{s}{\sqrt{n}}
\]
3. **Construct the confidence interval**:
\[
\bar{x} \pm (t \times SE)
\]
**Note:** Round the final answers to one decimal place as needed.
**Additional Resources:**
- Use the options "Help me solve this," "View an example," or "Get more help" for guided instruction and further understanding.
**Technical Note:**
Ensure your device's temperature remains optimal to facilitate smooth calculations.
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