MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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## Hypothesis Testing at α = 0.05 Significance Level **Objective:** Conduct a hypothesis test to determine whether \( p_1 \neq p_2 \). The sample data are as follows: \( x_1 = 28 \), \( n_1 = 255 \), \( x_2 = 38 \), \( n_2 = 302 \). Assume simple random sampling. ### Steps: ### (a) Determine the Null and Alternative Hypotheses: Choose the correct pair: - **A.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 < p_2 \) - **B.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 \neq p_2 \) - **C.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 > p_2 \) - **D.** \( H_0: p_1 = 0 \) versus \( H_1: p_1 = 0 \) ### (b) Test Statistic \( z_0 \): Calculate and fill in the test statistic value. - \( z_0 = \_ \) (Round to two decimal places as needed.) ### (c) P-value: Determine and input the P-value. - P-value = \_ (Round to three decimal places as needed.) ### Conclusion: Choose the correct conclusion about the null hypothesis: - **A.** Do not reject the null hypothesis because there is sufficient evidence to conclude that \( p_1 > p_2 \). - **B.** Reject the null hypothesis because there is sufficient evidence to conclude that \( p_1 \neq p_2 \). - **C.** Do not reject the null hypothesis because there is not sufficient evidence to conclude that \( p_1 \neq p_2 \). - **D.** Reject the null hypothesis because there is not sufficient evidence to conclude that \( p_1 < p_2 \).
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Transcribed Image Text:## Hypothesis Testing at α = 0.05 Significance Level **Objective:** Conduct a hypothesis test to determine whether \( p_1 \neq p_2 \). The sample data are as follows: \( x_1 = 28 \), \( n_1 = 255 \), \( x_2 = 38 \), \( n_2 = 302 \). Assume simple random sampling. ### Steps: ### (a) Determine the Null and Alternative Hypotheses: Choose the correct pair: - **A.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 < p_2 \) - **B.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 \neq p_2 \) - **C.** \( H_0: p_1 = p_2 \) versus \( H_1: p_1 > p_2 \) - **D.** \( H_0: p_1 = 0 \) versus \( H_1: p_1 = 0 \) ### (b) Test Statistic \( z_0 \): Calculate and fill in the test statistic value. - \( z_0 = \_ \) (Round to two decimal places as needed.) ### (c) P-value: Determine and input the P-value. - P-value = \_ (Round to three decimal places as needed.) ### Conclusion: Choose the correct conclusion about the null hypothesis: - **A.** Do not reject the null hypothesis because there is sufficient evidence to conclude that \( p_1 > p_2 \). - **B.** Reject the null hypothesis because there is sufficient evidence to conclude that \( p_1 \neq p_2 \). - **C.** Do not reject the null hypothesis because there is not sufficient evidence to conclude that \( p_1 \neq p_2 \). - **D.** Reject the null hypothesis because there is not sufficient evidence to conclude that \( p_1 < p_2 \).
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