Age of College Students Find the 80% confidence intervals for the variance and standard deviation of the ages of seniors at Oak Park College if a random sample of 28 students has a standard deviation of 2.5 years. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round the final answers to one decimal place. 0<<0 << X

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Age of College Students**

Find the 80% confidence intervals for the variance and standard deviation of the ages of seniors at Oak Park College if a random sample of 28 students has a standard deviation of 2.5 years. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round the final answers to one decimal place.

**Equation Layout:**
- \( \square < \sigma^2 < \square \)
- \( \square < \sigma < \square \)

**Explanation:**

The task requires you to compute the confidence intervals for both the variance (\(\sigma^2\)) and the standard deviation (\(\sigma\)) of a dataset. This is done using the chi-square distribution, which is appropriate for normally distributed variables like the ages mentioned in the problem. The given standard deviation of the sample is 2.5 years, and the sample size is 28 students. You need to refer to a chi-square distribution table to obtain the necessary chi-square values for calculating the intervals. The final result should be rounded to one decimal place.
Transcribed Image Text:**Age of College Students** Find the 80% confidence intervals for the variance and standard deviation of the ages of seniors at Oak Park College if a random sample of 28 students has a standard deviation of 2.5 years. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round the final answers to one decimal place. **Equation Layout:** - \( \square < \sigma^2 < \square \) - \( \square < \sigma < \square \) **Explanation:** The task requires you to compute the confidence intervals for both the variance (\(\sigma^2\)) and the standard deviation (\(\sigma\)) of a dataset. This is done using the chi-square distribution, which is appropriate for normally distributed variables like the ages mentioned in the problem. The given standard deviation of the sample is 2.5 years, and the sample size is 28 students. You need to refer to a chi-square distribution table to obtain the necessary chi-square values for calculating the intervals. The final result should be rounded to one decimal place.
Expert Solution
Step 1

The variable under consideration is normally distributed. 

Sample standard deviation is s=2.5

Sample size is n=28

confidence level is 80% that is, 1-α=0.80

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