**Hypothesis Testing Example: Testing if a Population Mean is Different from 8**Suppose there is a claim that a certain population has a mean, \(\mu\), that is different than 8. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.10 level of significance. To start this test, you write the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\) as follows:\[H_0: \mu = 8\]\[H_1: \mu \neq 8\]Suppose you also know the following information:- The critical values are \(-1.645\) and \(1.645\) (rounded to 3 decimal places).- The value of the test statistic is \(-1.198\) (rounded to 3 decimal places).### Part (a)**Complete the steps below to show the rejection region(s) and the value of the test statistic for this test.**A standard normal distribution graph is provided.**Steps:**1. **Select one-tailed or two-tailed:** Two-tailed2. **Enter the critical value(s):** -1.645 and 1.6453. **Enter the test statistic:** -1.198### Part (b)**Based on your answer to part (a), choose the correct statement.**- The value of the test statistic lies in the rejection region.- The value of the test statistic doesn’t lie in the rejection region. (chosen)### Part (c)**Based on your answer to part (b), which statement below is true at the 0.10 level of significance?**- The null hypothesis should be rejected.- The null hypothesis should not be rejected. (chosen)### Graph ExplanationThe graph shown is a bell-shaped curve representing a standard normal distribution. The x-axis ranges from approximately -3 to 3, and the y-axis shows the probability density. The critical values are marked at -1.645 and 1.645, indicating the boundaries of the rejection regions for this two-tailed test. The test statistic of -1.198 is plotted on the curve, not within the rejection regions, thus suggesting that the null hypothesis should not be rejected.

Given that Critical values = -1.645, 1.645 Test statistic = -1.198

Answered: (a) Complete the steps below to show…

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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