### Understanding Hypothesis Testing in StatisticsIn this example, we are analyzing a hypothesis test for the difference between two proportions.#### The Hypotheses- Null Hypothesis (H₀): \( p_1 - p_2 = 0 \)- Alternative Hypothesis (Hₐ): \( p_1 - p_2 \neq 0 \)This test is to determine if there is a significant difference between the two population proportions (\( p_1 \) and \( p_2 \)).#### Parameters Given- Significance level (\( \alpha \)): 0.10- Sample size for population 1 (\( n_1 \)): 500- Sample size for population 2 (\( n_2 \)): 523#### Determining the Critical ValueThe question asks: **What critical value forms the rejection region?**Let's break down the answer choices provided:- \( t = 1.645 \)- \( z = -1.645 \)- \( z = -1.645, z = 1.645 \)- \( t = -1.645, t = 1.645 \)Since the hypothesis involves comparing proportions, the appropriate test is a Z-test (rather than a T-test). The correct critical values, considering the two-tailed nature of our test (due to \( \neq \) in \( H_a \)), are based on the Z-distribution.For a significance level of 0.10 in a two-tailed test, the critical values are:- \( z = -1.645 \)- \( z = 1.645 \)Therefore, the correct answer is:- \( z = -1.645, z = 1.645 \)This option correctly represents the critical values for the rejection region in a two-tailed Z-test with an alpha level of 0.10.

The null and the alternate hypotheses indicates that it is case of test for a difference in…

Answered: We have this situation: Ho: P1 - P2 =…

We have this situation: Ho: P1 - P2 = 0, Ha: Pi – P2 # 0 a = 0.10 %3D ni = 500 %3D n2 = 523 What critical value forms the rejection region?

6th Edition

ISBN:9781119256830

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Chapter1: Starting With Matlab

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