**Hypothesis Testing with Significance Level 0.10****Step 3: Enter the Test Statistic** - Calculation: Round to 3 decimal places. - Test Statistic Value: 2.041**Visual Demonstration** The image includes two bell curves on either side of the test statistic:1. **Left Bell Curve:** - The area under the curve to the left of \( z_{\alpha/2} = -1.645 \) is shaded, indicating the rejection region on the negative side.2. **Right Bell Curve:** - The area under the curve to the right of \( z = 2.041 \) is shaded, marking the rejection region on the positive side. - The critical value is \( z_{\alpha/2} = 1.645 \).**Decision Making****(b) Analyzing the Test Statistic:**- Determine if the test statistic falls within the rejection region. - Options: - The value of the test statistic lies in the rejection region. - The value of the test statistic doesn't lie in the rejection region. - Response Options: Checkboxes next to each statement allow selection.**(c) Conclusion at 0.10 Level of Significance:**- Decide on the null hypothesis based on previous analysis. - Options: - The null hypothesis should be rejected. - The null hypothesis should not be rejected. - Response Options: Checkboxes next to each statement allow selection.**Interactive Elements**- Buttons for "Explanation" and "Check" findings.This layout and questioning guide students through the concepts of hypothesis testing, focusing on critical thinking and accurate decision-making based on statistical evidence in a two-tailed test. Suppose there is a claim that a certain population has a mean, μ, that is different than 9. 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:\[ H_0: \mu = 9 \]\[ H_1: \mu \neq 9 \]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 2.041 (rounded to 3 decimal places).(a) Complete the steps below to show the rejection region(s) and the value of the test statistic for this test.**Standard Normal Distribution**- **Step 1:** Select one-tailed or two-tailed. - One-tailed - Two-tailed (selected) - **Step 2:** Enter the critical value(s). (Round to 3 decimal places.) - -1.645, 1.645- **Step 3:** Enter the test statistic. (Round to 3 decimal places.) - 2.041**Graph Explanation:**The graph represents a standard normal distribution. It is a bell-shaped curve centered around a mean of 0. The x-axis represents the z-scores, while the y-axis represents the probability density. Critical values of -1.645 and 1.645 are marked on the x-axis, creating two rejection regions in the tails of the distribution. The test statistic of 2.041 is plotted on the x-axis, falling into the rejection region on the right side.

From the part a, The critical values are -1.645 and 1.645. Test statistic is 2.041.

Answered: (b) Based on your answer to part (a),…

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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Does more education lower a person’s level of prejudice? The number of years of education and the score on a prejudice test for ten people is given in the following table. Higher scores on the test indicate more prejudice. Years of Education: 12, 15, 14, 13, 18, 10, 16, 12, 10, 4 Score of Prejudice Test: 1, 6, 2, 3, 2, 4, 1, 5, 5, 10 Conduct a hypothesis test to determine if there is a significant linear correlation between the two variables. If there is a significant linear correlation between the variables, determine the regression equation. There is a significant correlation between the variables and the regression equation is y' = 10.5 - 0.532x There is a significant correlation between the variables and the regression equation is y' = - 0.532 + 10.5x There is not a significant correlation between the variables, so the regression equation should not be determined. There is a significant correlation between the variables and the regression equation is y' = 16.509 - 1.054x
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(b) Based on your answer to part (a), choose the correct statement. The value of the test statistic lies in the rejection region. O The value of the test statistic doesn't lie in the rejection region. S