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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<

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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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.
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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