If n-27, (x-bar)=42, and s-4, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place. <μ<
If n-27, (x-bar)=42, and s-4, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place. <μ<
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
**Problem Statement:**
Given the following statistical data:
- Sample size (\(n\)) = 27
- Sample mean (\(\bar{x}\)) = 42
- Sample standard deviation (\(s\)) = 4
Construct a confidence interval at a 99% confidence level, assuming the data came from a normally distributed population.
**Instructions:**
Calculate the confidence interval for the population mean (\(\mu\)) and provide the answers rounded to one decimal place.
**Solution:**
To construct the confidence interval, follow these steps:
1. **Identify the sample statistics:**
- Sample size (\(n\)) = 27
- Sample mean (\(\bar{x}\)) = 42
- Sample standard deviation (\(s\)) = 4
2. **Determine the critical value:**
- For a 99% confidence level with 26 degrees of freedom (\(df\)), use the t-distribution to find the critical value (\(t^*\)).
3. **Calculate the margin of error (ME):**
\[\text{ME} = t^* \times \left(\frac{s}{\sqrt{n}}\right)\]
4. **Construct the confidence interval:**
\[
\bar{x} - \text{ME} < \mu < \bar{x} + \text{ME}
\]
Since this is an educational site, it is expected that the user will perform these calculations or the steps might be demonstrated in the subsequent steps of the lesson.
5. **Final Solution Box:**
Users will input their computed confidence interval here:
\[
< \mu <
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Transcribed Image Text:### Constructing a Confidence Interval
**Problem Statement:**
Given the following statistical data:
- Sample size (\(n\)) = 27
- Sample mean (\(\bar{x}\)) = 42
- Sample standard deviation (\(s\)) = 4
Construct a confidence interval at a 99% confidence level, assuming the data came from a normally distributed population.
**Instructions:**
Calculate the confidence interval for the population mean (\(\mu\)) and provide the answers rounded to one decimal place.
**Solution:**
To construct the confidence interval, follow these steps:
1. **Identify the sample statistics:**
- Sample size (\(n\)) = 27
- Sample mean (\(\bar{x}\)) = 42
- Sample standard deviation (\(s\)) = 4
2. **Determine the critical value:**
- For a 99% confidence level with 26 degrees of freedom (\(df\)), use the t-distribution to find the critical value (\(t^*\)).
3. **Calculate the margin of error (ME):**
\[\text{ME} = t^* \times \left(\frac{s}{\sqrt{n}}\right)\]
4. **Construct the confidence interval:**
\[
\bar{x} - \text{ME} < \mu < \bar{x} + \text{ME}
\]
Since this is an educational site, it is expected that the user will perform these calculations or the steps might be demonstrated in the subsequent steps of the lesson.
5. **Final Solution Box:**
Users will input their computed confidence interval here:
\[
< \mu <
\]
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