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Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.89 versus H₁: p=0.89 n = 500, x=440, α = 0.01 Is npo (1-Po) 210? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) OA. Yes, because npo (1-P) = OB. No, because npo (1-P) =

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.89 versus H₁: p=0.89 n = 500, x=440, α = 0.01 Is npo (1-Po) 210? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) OA. Yes, because npo (1-P) = OB. No, because npo (1-P) =

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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**Hypothesis Testing Using the P-Value Approach** To test the hypothesis using the P-value approach, we have the following setup: - Null hypothesis (\(H_0\)): \( p = 0.89 \) - Alternative hypothesis (\(H_1\)): \( p \neq 0.89 \) Given data: - Sample size (\(n\)): 500 - Number of successes (\(x\)): 440 - Significance level (\(\alpha\)): 0.01 **Verification Requirement** We need to verify that \(np_0(1 - p_0) \geq 10\). Please select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) - A. Yes, because \(np_0(1 - p_0) =\) [ ] - B. No, because \(np_0(1 - p_0) =\) [ ] Please compute \(np_0(1 - p_0)\) with the given values to verify the requirement.
Transcribed Image Text:**Hypothesis Testing Using the P-Value Approach** To test the hypothesis using the P-value approach, we have the following setup: - Null hypothesis (\(H_0\)): \( p = 0.89 \) - Alternative hypothesis (\(H_1\)): \( p \neq 0.89 \) Given data: - Sample size (\(n\)): 500 - Number of successes (\(x\)): 440 - Significance level (\(\alpha\)): 0.01 **Verification Requirement** We need to verify that \(np_0(1 - p_0) \geq 10\). Please select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) - A. Yes, because \(np_0(1 - p_0) =\) [ ] - B. No, because \(np_0(1 - p_0) =\) [ ] Please compute \(np_0(1 - p_0)\) with the given values to verify the requirement.
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Step 1: Given data,

H y p o t h e s i s colon H subscript 0 colon p equals 0.89 H subscript 1 colon p space not equal to 0.89 A space s a m p l e space s i z e colon n equals 500 f a v o r a b l e space o u t c o m e s colon x equals 440 T h e space l e v e l space o f space s i g n i f i c a n c e colon alpha equals 0.01

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**Hypothesis Testing Using the P-value Approach** **Objective:** Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. **Hypotheses:** - Null Hypothesis (\(H_0\)): \(p = 0.89\) - Alternative Hypothesis (\(H_1\)): \(p \neq 0.89\) **Given:** - Sample size (\(n\)) = 500 - Number of successes (\(x\)) = 440 - Significance level (\(\alpha\)) = 0.01 **Step 1: Verify Conditions** Determine if \(np_0(1 - p_0) \geq 10\). 1. Calculate \(np_0(1 - p_0)\): \[ np_0(1 - p_0) = 48.95 \] Choice A is chosen: *Yes, because \(np_0(1 - p_0) = 48.95\).* **Step 2: Find \(\hat{p}\)** Calculate the sample proportion (\(\hat{p}\)): - \(\hat{p} = 0.88\) **Step 3: Find the Test Statistic \(z_0\)** Calculate the test statistic: - \(z_0 = -0.72\) - (Rounded to two decimal places as needed.) **Step 4: Find the P-value** The P-value will need to be calculated to three decimal places as needed. --- **Summary:** This step-by-step guide helps in conducting a hypothesis test using the P-value approach by verifying the necessary conditions, calculating the sample proportion, finding the test statistic, and determining the P-value. Ensure all values are rounded to the specified precision for accuracy.
Transcribed Image Text:**Hypothesis Testing Using the P-value Approach** **Objective:** Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. **Hypotheses:** - Null Hypothesis (\(H_0\)): \(p = 0.89\) - Alternative Hypothesis (\(H_1\)): \(p \neq 0.89\) **Given:** - Sample size (\(n\)) = 500 - Number of successes (\(x\)) = 440 - Significance level (\(\alpha\)) = 0.01 **Step 1: Verify Conditions** Determine if \(np_0(1 - p_0) \geq 10\). 1. Calculate \(np_0(1 - p_0)\): \[ np_0(1 - p_0) = 48.95 \] Choice A is chosen: *Yes, because \(np_0(1 - p_0) = 48.95\).* **Step 2: Find \(\hat{p}\)** Calculate the sample proportion (\(\hat{p}\)): - \(\hat{p} = 0.88\) **Step 3: Find the Test Statistic \(z_0\)** Calculate the test statistic: - \(z_0 = -0.72\) - (Rounded to two decimal places as needed.) **Step 4: Find the P-value** The P-value will need to be calculated to three decimal places as needed. --- **Summary:** This step-by-step guide helps in conducting a hypothesis test using the P-value approach by verifying the necessary conditions, calculating the sample proportion, finding the test statistic, and determining the P-value. Ensure all values are rounded to the specified precision for accuracy.
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Follow-up Question
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.89 versus H₁: p#0.89 1 = 500, x= 440, a = 0.01 Is npo (1-Po) ²10? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. Yes, because npo (1-Po) = 48.95 OB. No, because npo (1-Po) = Now find p p= 0.88 (Type an integer or a decimal. Do not round.) Find the test statistic zo. Zo = (Round to two decimal places as needed.) W ---
Transcribed Image Text:Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.89 versus H₁: p#0.89 1 = 500, x= 440, a = 0.01 Is npo (1-Po) ²10? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. Yes, because npo (1-Po) = 48.95 OB. No, because npo (1-Po) = Now find p p= 0.88 (Type an integer or a decimal. Do not round.) Find the test statistic zo. Zo = (Round to two decimal places as needed.) W ---
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Follow-up Question
**Hypothesis Testing Using the P-Value Approach** *Question:* Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. - Null Hypothesis (\(H_0\)): \(p = 0.89\) - Alternative Hypothesis (\(H_1\)): \(p \neq 0.89\) - Sample size (\(n\)): 500 - Number of successes (\(x\)): 440 - Significance level (\(\alpha\)): 0.01 **Verification:** Check if \(np_0(1 - p_0) \geq 10\). Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) - A. Yes, because \(np_0(1 - p_0) = 48.95\). [This option is selected] - B. No, because \(np_0(1 - p_0) = \_\_\_ \). **Next Step:** Now find \(\hat{p}\). - \(\hat{p} = \_\_\_\) (Type an integer or a decimal. Do not round.)
Transcribed Image Text:**Hypothesis Testing Using the P-Value Approach** *Question:* Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. - Null Hypothesis (\(H_0\)): \(p = 0.89\) - Alternative Hypothesis (\(H_1\)): \(p \neq 0.89\) - Sample size (\(n\)): 500 - Number of successes (\(x\)): 440 - Significance level (\(\alpha\)): 0.01 **Verification:** Check if \(np_0(1 - p_0) \geq 10\). Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) - A. Yes, because \(np_0(1 - p_0) = 48.95\). [This option is selected] - B. No, because \(np_0(1 - p_0) = \_\_\_ \). **Next Step:** Now find \(\hat{p}\). - \(\hat{p} = \_\_\_\) (Type an integer or a decimal. Do not round.)
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