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Test the following hypotheses by using the \( \chi^2 \) goodness of fit test. - \( H_0: P_A = 0.40, \, P_B = 0.40, \, \text{and} \, P_C = 0.20 \) - \( H_a: \) The population proportions are not \( P_A = 0.40, \, P_B = 0.40, \, \text{and} \, P_C = 0.20 \). A sample of size 200 yielded 40 in category A, 140 in category B, and 20 in category C. Use \( \alpha = 0.01 \) and test to see whether the proportions are as stated in \( H_0 \). ### (a) Use the \( p \)-value approach. - **Find the value of the test statistic.** \( \text{Test statistic} = \underline{\phantom{Answer}}\) - **Find the \( p \)-value.** (Round your answer to four decimal places.) \( p=\text{-value} = \underline{\phantom{Answer}} \) - **State your conclusion.** - \( \circ \) Reject \( H_0 \). We conclude that the proportions differ from 0.40, 0.40, and 0.20. - \( \circ \) Reject \( H_0 \). We conclude that the proportions are equal to 0.40, 0.40, and 0.20. - \( \circ \) Do not reject \( H_0 \). We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. - \( \circ \) Do not reject \( H_0 \). We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. ### (b) Repeat the test using the critical value approach. - **Find the value of the test statistic.** \( \text{Test statistic} = \underline{\phantom{Answer}} \) - **State the critical values for the rejection rule.** (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.) \( \text{Test statistic} \leq \underline

Test the following hypotheses by using the \( \chi^2 \) goodness of fit test. - \( H_0: P_A = 0.40, \, P_B = 0.40, \, \text{and} \, P_C = 0.20 \) - \( H_a: \) The population proportions are not \( P_A = 0.40, \, P_B = 0.40, \, \text{and} \, P_C = 0.20 \). A sample of size 200 yielded 40 in category A, 140 in category B, and 20 in category C. Use \( \alpha = 0.01 \) and test to see whether the proportions are as stated in \( H_0 \). ### (a) Use the \( p \)-value approach. - **Find the value of the test statistic.** \( \text{Test statistic} = \underline{\phantom{Answer}}\) - **Find the \( p \)-value.** (Round your answer to four decimal places.) \( p=\text{-value} = \underline{\phantom{Answer}} \) - **State your conclusion.** - \( \circ \) Reject \( H_0 \). We conclude that the proportions differ from 0.40, 0.40, and 0.20. - \( \circ \) Reject \( H_0 \). We conclude that the proportions are equal to 0.40, 0.40, and 0.20. - \( \circ \) Do not reject \( H_0 \). We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. - \( \circ \) Do not reject \( H_0 \). We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. ### (b) Repeat the test using the critical value approach. - **Find the value of the test statistic.** \( \text{Test statistic} = \underline{\phantom{Answer}} \) - **State the critical values for the rejection rule.** (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.) \( \text{Test statistic} \leq \underline

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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Test the following hypotheses by using the \( \chi^2 \) goodness of fit test. - \( H_0: P_A = 0.40, \, P_B = 0.40, \, \text{and} \, P_C = 0.20 \) - \( H_a: \) The population proportions are not \( P_A = 0.40, \, P_B = 0.40, \, \text{and} \, P_C = 0.20 \). A sample of size 200 yielded 40 in category A, 140 in category B, and 20 in category C. Use \( \alpha = 0.01 \) and test to see whether the proportions are as stated in \( H_0 \). ### (a) Use the \( p \)-value approach. - **Find the value of the test statistic.** \( \text{Test statistic} = \underline{\phantom{Answer}}\) - **Find the \( p \)-value.** (Round your answer to four decimal places.) \( p=\text{-value} = \underline{\phantom{Answer}} \) - **State your conclusion.** - \( \circ \) Reject \( H_0 \). We conclude that the proportions differ from 0.40, 0.40, and 0.20. - \( \circ \) Reject \( H_0 \). We conclude that the proportions are equal to 0.40, 0.40, and 0.20. - \( \circ \) Do not reject \( H_0 \). We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. - \( \circ \) Do not reject \( H_0 \). We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. ### (b) Repeat the test using the critical value approach. - **Find the value of the test statistic.** \( \text{Test statistic} = \underline{\phantom{Answer}} \) - **State the critical values for the rejection rule.** (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.) \( \text{Test statistic} \leq \underline
Transcribed Image Text:Test the following hypotheses by using the \( \chi^2 \) goodness of fit test. - \( H_0: P_A = 0.40, \, P_B = 0.40, \, \text{and} \, P_C = 0.20 \) - \( H_a: \) The population proportions are not \( P_A = 0.40, \, P_B = 0.40, \, \text{and} \, P_C = 0.20 \). A sample of size 200 yielded 40 in category A, 140 in category B, and 20 in category C. Use \( \alpha = 0.01 \) and test to see whether the proportions are as stated in \( H_0 \). ### (a) Use the \( p \)-value approach. - **Find the value of the test statistic.** \( \text{Test statistic} = \underline{\phantom{Answer}}\) - **Find the \( p \)-value.** (Round your answer to four decimal places.) \( p=\text{-value} = \underline{\phantom{Answer}} \) - **State your conclusion.** - \( \circ \) Reject \( H_0 \). We conclude that the proportions differ from 0.40, 0.40, and 0.20. - \( \circ \) Reject \( H_0 \). We conclude that the proportions are equal to 0.40, 0.40, and 0.20. - \( \circ \) Do not reject \( H_0 \). We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. - \( \circ \) Do not reject \( H_0 \). We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. ### (b) Repeat the test using the critical value approach. - **Find the value of the test statistic.** \( \text{Test statistic} = \underline{\phantom{Answer}} \) - **State the critical values for the rejection rule.** (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.) \( \text{Test statistic} \leq \underline
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