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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?

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?

MATLAB: An Introduction with Applications
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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### Understanding Hypothesis Testing in Statistics In 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 Value The 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.
Transcribed Image Text:### Understanding Hypothesis Testing in Statistics In 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 Value The 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.
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