### Constructing Confidence Intervals for Population Variance and Standard DeviationIn this lesson, we will demonstrate how to use technology to construct the confidence intervals for the population variance (\(\sigma^2\)) and the population standard deviation (\(\sigma\)). Assume that the sample is taken from a normally distributed population.Given data:- Confidence level (\(c\)) = 0.90- Sample variance (\(s^2\)) = 6.25- Sample size (\(n\)) = 25#### Task:1. **Confidence Interval for Population Variance (\(\sigma^2\))**\[ \text{The confidence interval for the population variance is } \left( \,\,\_,\,\,\, \_\,\_ \right) \]*(Round to two decimal places as needed.)*2. **Confidence Interval for Population Standard Deviation (\(\sigma\))**\[ \text{The confidence interval for the population standard deviation is } \left( \,\,\_,\,\,\, \_\,\_ \right) \]*(Round to two decimal places as needed.)*To accurately determine these intervals, you would typically use statistical software or graphing calculators capable of handling such computations. The process involves using the sample variance, the sample size, and the chi-square distribution corresponding to the selected confidence level to find the required confidence intervals.### Steps to calculate the confidence intervals:1: **Identify the chi-square critical values:** Corresponding to the desired confidence level and degrees of freedom (\(df = n-1 = 24\)).2: **Calculate the confidence interval for the variance (\(\sigma^2\)):**\[ \frac{(n-1)s^2}{\chi^2_{\alpha/2}} < \sigma^2 < \frac{(n-1)s^2}{\chi^2_{(1-\alpha/2)}} \]3: **Calculate the confidence interval for the standard deviation (\(\sigma\)) by taking the square root of the interval found for the variance.**

Use technology to construct the confidence intervals for the population variance o? and the population standard deviation o. Assume the sample is taken from a normally distributed population. c= 0.90, s? = 6.25, n = 25 The confidence interval for the population variance is ( ). (Round to two decimal places as needed.)

Use technology to construct the confidence intervals for the population variance o? and the population standard deviation o. Assume the sample is taken from a normally distributed population. c= 0.90, s? = 6.25, n = 25 The confidence interval for the population variance is ( ). (Round to two decimal places as needed.)

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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