**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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This assignment is worth 1 points. The extra point will be added to your overall course grade. For example: if you receive an 88% in the course you can receive up to 1 point giving you a new score of 89%. The following rubric will be used. 0.25 point for drawing the normal distribution curve with the mean value labeled on the curve and the appropriate area shaded. 0.25 point for determining the value of the standard deviation of the sample mean. 0.5 point for finding the correct probability. All work must be shown in order to receive any credit. Please upload your completed assignment here. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.
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