### Understanding Critical Values in Hypothesis Testing**Problem Statement:**Assume that the data has a normal distribution and the number of observations is 20. Find the critical value used to test a null hypothesis about the population mean, if the significance level is \( \alpha = 0.05 \); and \( H_1: \mu > 3.24 \)**Options:**A. 1.729 B. 2.086 C. 2.093 D. 1.833 **Explanation:**To solve this problem, you need to understand the concept of critical values in hypothesis testing. Specifically, we are dealing with a one-tailed test (since \( H_1: \mu > 3.24 \)) at a significance level (\(\alpha\)) of 0.05. Since the sample size (n) is 20, we will likely use a t-distribution to find the critical value.**Steps to Solve:**1. **Identify the degrees of freedom (df):** Degrees of freedom for a t-test is given by \( df = n - 1 \). Here, \( df = 20 - 1 = 19 \).2. **Determine the critical value for a one-tailed test:** At a significance level of \( \alpha = 0.05 \) for a one-tailed test, you'd look up the critical value in a t-distribution table for 19 degrees of freedom.By referring to the t-distribution table or using statistical software:- A critical value for \( df = 19 \) and \(\alpha = 0.05 \) in a one-tailed test is approximately 1.729.Therefore, the correct answer is:**A. 1.729**This critical value indicates that, for a sample of 20 observations, if the sample mean is greater than this critical value, the null hypothesis \( H_0 \) would be rejected in favor of the alternative hypothesis \( H_1: \mu > 3.24 \).Use this information to correctly apply the concept of critical values in hypothesis testing scenarios.

Given that The data followed normal distribution.Number of observations (n) = 20Level of…

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Assume that the data has a normal distribution and the number of observations is 20. Find the critical value used to test a null hypothesis about the population mean, if the significance level is a-0.05; and Hl:p>3.24