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The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.34. Construct a 95% two-sided confidence interval for o. Assume population is approximately normally distributed. Round your answers to 4 decimal places. sos i

The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.34. Construct a 95% two-sided confidence interval for o. Assume population is approximately normally distributed. Round your answers to 4 decimal places. sos i

MATLAB: An Introduction with Applications
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 Standard Deviation **Problem Statement:** The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is \( s = 0.34 \). Construct a 95% two-sided confidence interval for \( \sigma \) (the population standard deviation). Assume the population is approximately normally distributed. **Instructions:** - Round your answers to 4 decimal places. - Use the formula and relevant statistical tables to calculate the interval. **Input Fields:** There are two input boxes provided: - The lower bound of the confidence interval - The upper bound of the confidence interval **Additional Resources:** - A link is provided to "Statistical Tables and Charts" for reference in calculations. ### Explanation The task involves statistical analysis to construct a confidence interval for the population standard deviation (\( \sigma \)) based on a given sample standard deviation (\( s \)) and sample size. A 95% confidence interval gives a range in which the true standard deviation is likely to lie with 95% probability. Utilizing a chi-square distribution due to the assumption of normality, you'll determine the critical values to compute the confidence bounds. Use the provided statistical resources for guidance.
Transcribed Image Text:### Constructing a Confidence Interval for the Standard Deviation **Problem Statement:** The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is \( s = 0.34 \). Construct a 95% two-sided confidence interval for \( \sigma \) (the population standard deviation). Assume the population is approximately normally distributed. **Instructions:** - Round your answers to 4 decimal places. - Use the formula and relevant statistical tables to calculate the interval. **Input Fields:** There are two input boxes provided: - The lower bound of the confidence interval - The upper bound of the confidence interval **Additional Resources:** - A link is provided to "Statistical Tables and Charts" for reference in calculations. ### Explanation The task involves statistical analysis to construct a confidence interval for the population standard deviation (\( \sigma \)) based on a given sample standard deviation (\( s \)) and sample size. A 95% confidence interval gives a range in which the true standard deviation is likely to lie with 95% probability. Utilizing a chi-square distribution due to the assumption of normality, you'll determine the critical values to compute the confidence bounds. Use the provided statistical resources for guidance.
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