**Hypothesis Testing: Finding the Critical Value**In this example, we will explore a situation involving hypothesis testing. We are given the following conditions:- Null Hypothesis (\(H_0\)): \(\mu = 100\)- Alternative Hypothesis (\(H_a\)): \(\mu > 100\)- Significance Level (\(\alpha\)): 0.05- Sample Size (\(n\)): 32The challenge is to determine the critical value that forms the rejection region for this hypothesis test.**Choices Provided:**1. \( \boxed{z = 1.645} \)2. \( \boxed{z = 1.960} \)3. \( \boxed{t = 1.960} \)4. \( \boxed{t = 1.645} \)In hypothesis testing for a population mean, the critical value determines the threshold at which we reject the null hypothesis in favor of the alternative hypothesis. The choice of \(z\)-score or \(t\)-score depends on the sample size and whether the population standard deviation is known.**Explanation of Choices:**- \(z\)-scores are typically used when the sample size is large (usually \(n \geq 30\)) and/or the population standard deviation is known.- \(t\)-scores are used when the sample size is small and/or the population standard deviation is unknown.Given:- The sample size here is 32, which is typically considered large enough to use the \(z\)-distribution.Since we are performing a one-tailed test at \(\alpha = 0.05\), the critical \(z\)-value that corresponds to this significance level (5%) in a standard normal distribution is approximately 1.645.Therefore, the appropriate critical value for this scenario is:\[ \boxed{z = 1.645} \]In conclusion, the value \(z = 1.645\) forms the rejection region for this hypothesis test, meaning that if the test statistic exceeds 1.645, we reject the null hypothesis in favor of the alternative hypothesis.

Given information Sample size n = 32 Significance level (α) = 0.05 Null and Alternative Hypothesis…

Answered: We have this situation: Ho: H = 100 H:…

Math

Statistics

We have this situation: Ho: H = 100 H: H > 100 a = 0.05 n = 32 What critical value forms the rejection region?

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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