If n=32, x(x-bar)=47, and s=18, 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=32, x(x-bar)=47, and s=18, 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<
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Constructing a Confidence Interval at a 99% Confidence Level
**Problem Statement:**
Given the following information:
- Sample size (n) = 32
- Sample mean (\(\bar{x}\)) = 47
- Sample standard deviation (s) = 18
Construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population.
**Instructions:**
1. **Identify the Sample Requirements:**
- Sample Size (\(n\)): 32
- Sample Mean (\(\bar{x}\)): 47
- Sample Standard Deviation (\(s\)): 18
2. **Select the Confidence Level:**
- Confidence Level = 99%
3. **Determine the Appropriate t-Score:**
- For a 99% confidence level and degrees of freedom (df) of \(n-1 = 31\), the t-score can be obtained from t-distribution tables or calculators.
4. **Calculate the Margin of Error (ME):**
- ME = \(t \times \frac{s}{\sqrt{n}}\)
where \(t\) is the t-score for 99% confidence and 31 degrees of freedom.
5. **Construct the Confidence Interval:**
- Confidence Interval = \(\bar{x} \pm \text{ME}\)
6. **Provide the Final Answer:**
- Ensure the answers are given to one decimal place.
**Answer Format:**
\[ \text{Lower Bound} < \mu < \text{Upper Bound} \]
(The actual numerical solutions are not provided as the application requires the interpretation of the image.)
These steps outline how one constructs the confidence interval given the statistical data and the requirements. By following this procedure, you can determine the range within which the true population mean is expected to lie with 99% confidence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e97f72a-1c8d-4466-a361-8c71e85dddcc%2F4ac39f33-02cc-4812-b468-343183a03f9c%2F0jayi2_processed.png&w=3840&q=75)
Transcribed Image Text:### Constructing a Confidence Interval at a 99% Confidence Level
**Problem Statement:**
Given the following information:
- Sample size (n) = 32
- Sample mean (\(\bar{x}\)) = 47
- Sample standard deviation (s) = 18
Construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population.
**Instructions:**
1. **Identify the Sample Requirements:**
- Sample Size (\(n\)): 32
- Sample Mean (\(\bar{x}\)): 47
- Sample Standard Deviation (\(s\)): 18
2. **Select the Confidence Level:**
- Confidence Level = 99%
3. **Determine the Appropriate t-Score:**
- For a 99% confidence level and degrees of freedom (df) of \(n-1 = 31\), the t-score can be obtained from t-distribution tables or calculators.
4. **Calculate the Margin of Error (ME):**
- ME = \(t \times \frac{s}{\sqrt{n}}\)
where \(t\) is the t-score for 99% confidence and 31 degrees of freedom.
5. **Construct the Confidence Interval:**
- Confidence Interval = \(\bar{x} \pm \text{ME}\)
6. **Provide the Final Answer:**
- Ensure the answers are given to one decimal place.
**Answer Format:**
\[ \text{Lower Bound} < \mu < \text{Upper Bound} \]
(The actual numerical solutions are not provided as the application requires the interpretation of the image.)
These steps outline how one constructs the confidence interval given the statistical data and the requirements. By following this procedure, you can determine the range within which the true population mean is expected to lie with 99% confidence.
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