Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.81 versus H₁: p=0.81 n=500, x=390, α=0.05 ... s npo (1-Po) ≥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. No, because npo (1-Po) B. Yes, because npo (1-Po) = 76.95 ow find p = 0.780 (Type an integer or a decimal. Do not round.) nd the test statistic Zo- 4 = -1.71 (Round to two decimal places as needed.) nd the P-value. value= (Round to three decimal places as needed.)
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.81 versus H₁: p=0.81 n=500, x=390, α=0.05 ... s npo (1-Po) ≥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. No, because npo (1-Po) B. Yes, because npo (1-Po) = 76.95 ow find p = 0.780 (Type an integer or a decimal. Do not round.) nd the test statistic Zo- 4 = -1.71 (Round to two decimal places as needed.) nd the P-value. value= (Round to three decimal places as needed.)
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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I need help finding the p value. Thank you.
![## Hypothesis Testing Using the P-Value Approach
**Objective:** Test the hypothesis using the P-value approach and verify the requirements of the test.
**Given Data:**
- Null hypothesis \( H_0: p = 0.81 \)
- Alternative hypothesis \( H_1: p \ne 0.81 \)
- Sample size \( n = 500 \)
- Number of successes \( x = 390 \)
- Significance level \( \alpha = 0.05 \)
**Step-by-Step Procedure:**
1. **Verify Sample Size Requirement:**
\[
n p_0 (1 - p_0) \ge 10
\]
- Calculation:
\[
n p_0 (1 - p_0) = 500 \times 0.81 \times (1 - 0.81) = 500 \times 0.81 \times 0.19 = 76.95
\]
- Conclusion:
\[
\text{Yes, because } n p_0 (1 - p_0) = 76.95
\]
2. **Calculate \( \hat{p} \):**
\[
\hat{p} = \frac{x}{n} = \frac{390}{500} = 0.780
\]
*(Type as an integer or a decimal. Do not round.)*
3. **Compute the Test Statistic \( z_0 \):**
\[
z_0 = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
\]
- Calculation:
\[
z_0 = \frac{0.780 - 0.81}{\sqrt{\frac{0.81 \times 0.19}{500}}} = \frac{-0.03}{\sqrt{\frac{0.1539}{500}}} = \frac{-0.03}{\sqrt{0.0003078}} = \frac{-0.03}{0.01754} \approx -1.71
\]
*(Round to two decimal places as needed.)*
4. **Determine the P-value:**
\[
\text{P-value} = (Round to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F254f01d1-5636-4aee-8bdd-3770d49eb7a5%2F46a2a3e0-f243-455a-84ec-9b3c523849ea%2F6n758vs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Hypothesis Testing Using the P-Value Approach
**Objective:** Test the hypothesis using the P-value approach and verify the requirements of the test.
**Given Data:**
- Null hypothesis \( H_0: p = 0.81 \)
- Alternative hypothesis \( H_1: p \ne 0.81 \)
- Sample size \( n = 500 \)
- Number of successes \( x = 390 \)
- Significance level \( \alpha = 0.05 \)
**Step-by-Step Procedure:**
1. **Verify Sample Size Requirement:**
\[
n p_0 (1 - p_0) \ge 10
\]
- Calculation:
\[
n p_0 (1 - p_0) = 500 \times 0.81 \times (1 - 0.81) = 500 \times 0.81 \times 0.19 = 76.95
\]
- Conclusion:
\[
\text{Yes, because } n p_0 (1 - p_0) = 76.95
\]
2. **Calculate \( \hat{p} \):**
\[
\hat{p} = \frac{x}{n} = \frac{390}{500} = 0.780
\]
*(Type as an integer or a decimal. Do not round.)*
3. **Compute the Test Statistic \( z_0 \):**
\[
z_0 = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}
\]
- Calculation:
\[
z_0 = \frac{0.780 - 0.81}{\sqrt{\frac{0.81 \times 0.19}{500}}} = \frac{-0.03}{\sqrt{\frac{0.1539}{500}}} = \frac{-0.03}{\sqrt{0.0003078}} = \frac{-0.03}{0.01754} \approx -1.71
\]
*(Round to two decimal places as needed.)*
4. **Determine the P-value:**
\[
\text{P-value} = (Round to three decimal places as needed.)
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