### Hypothesis Testing for a Normal Distribution#### OverviewA random sample of size 8 from a normal distribution has a standard deviation $ s = 89 $. We are testing the null hypothesis $ H_0: \sigma = 41 $ versus the alternative hypothesis $ H_1: \sigma < 41 $. The level of significance for the test is $ \alpha = 0.05 $.#### Part 1 of 5The hypotheses are provided above. This hypothesis test is a **left-tailed** test.#### Part 2 of 5Find the critical value.- **Critical value**: 2.167#### Part 3 of 5Compute the test statistic. Round the answer to three decimal places as needed.- $ \chi^2 = $ _______#### Graphical RepresentationThere are no explanatory graphs or diagrams included in this problem. It is purely based on hypothesis testing using the chi-square distribution.#### Further StepsTo proceed, compute the test statistic utilizing the given information:1. Sample size ($ n = 8 $)2. Sample standard deviation ($ s = 89 $)3. Null hypothesis standard deviation ($ \sigma = 41 $)Use the formula for the chi-square test statistic for standard deviation:\[ \chi^2 = \frac{(n-1)s^2}{\sigma^2} \]Substitute the values and compute the test statistic, then compare it with the critical value to determine whether to reject the null hypothesis.

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A random sample of size 8 from a normal distribution has standard deviation s 89. Test H:0=41 versus H: o<41. Use the a 0.05 level of significance. Part 1 of 5 The hypotheses are provided above. This hypothesis test is a left-tailed test. Part 2 of 5 Find the critical value. Critical value= 2.167 Part: 2/5 Part 3 of 5 Compute the test statistic. Round the answer to three decimal places as needed.

A random sample of size 8 from a normal distribution has standard deviation s 89. Test H:0=41 versus H: o<41. Use the a 0.05 level of significance. Part 1 of 5 The hypotheses are provided above. This hypothesis test is a left-tailed test. Part 2 of 5 Find the critical value. Critical value= 2.167 Part: 2/5 Part 3 of 5 Compute the test statistic. Round the answer to three 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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