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, a = 0.05 Is 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.) OA. No, because npo (1-Po) B. Yes, because npo (1-Po) = 76.95. Now find p. (Type an integer or a decimal. Do not round)
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, a = 0.05 Is 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.) OA. No, because npo (1-Po) B. Yes, because npo (1-Po) = 76.95. Now find p. (Type an integer or a decimal. Do not round)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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I need help finding P.
![### Hypothesis Testing Using the P-Value Approach
**Problem Statement:**
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
- Null Hypothesis (H₀): p = 0.81
- Alternative Hypothesis (H₁): p ≠ 0.81
- Given values:
- n = 500
- x = 390
- α (alpha) = 0.05
### Step 1: Verify Test Requirements
Is \( np_0(1 - p_0) \geq 10 \)?
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Do not round.)
- **Option A:** No, because \( np_0(1 - p_0) = \_\_\_ \)
- **Option B:** Yes, because \( np_0(1 - p_0) = 76.95 \)
*(The correct choice is Option B)*
### Step 2: Calculate Sample Proportion (\(\hat{p}\))
\[
\hat{p} = \frac{x}{n}
\]
Type the value of \(\hat{p}\) as an integer or a decimal. Do not round.
\[
\hat{p} = \_\_\_
\]
---
**Explanation:**
1. **Verification:**
- Calculate \( np_0(1 - p_0) \):
\[
np_0(1 - p_0) = 500 \times 0.81 \times (1 - 0.81) = 500 \times 0.81 \times 0.19 = 76.95
\]
- Since \( 76.95 \geq 10 \), the requirement is met. Therefore, the correct choice is:
- **Option B:** Yes, because \( np_0(1 - p_0) = 76.95 \)
2. **Sample Proportion:**
- Calculate the sample proportion \(\hat{p}\):
\[
\hat{p} = \frac{390}{500} = 0.78
\]
- Enter \(\hat{p}\) as 0.78 in the answer box.
---
**Visual Aids:** No graphs or diagrams](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F254f01d1-5636-4aee-8bdd-3770d49eb7a5%2F4c951e96-5f15-4cdf-a696-f16e45a850f8%2Fpbn95o7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Using the P-Value Approach
**Problem Statement:**
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
- Null Hypothesis (H₀): p = 0.81
- Alternative Hypothesis (H₁): p ≠ 0.81
- Given values:
- n = 500
- x = 390
- α (alpha) = 0.05
### Step 1: Verify Test Requirements
Is \( np_0(1 - p_0) \geq 10 \)?
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Do not round.)
- **Option A:** No, because \( np_0(1 - p_0) = \_\_\_ \)
- **Option B:** Yes, because \( np_0(1 - p_0) = 76.95 \)
*(The correct choice is Option B)*
### Step 2: Calculate Sample Proportion (\(\hat{p}\))
\[
\hat{p} = \frac{x}{n}
\]
Type the value of \(\hat{p}\) as an integer or a decimal. Do not round.
\[
\hat{p} = \_\_\_
\]
---
**Explanation:**
1. **Verification:**
- Calculate \( np_0(1 - p_0) \):
\[
np_0(1 - p_0) = 500 \times 0.81 \times (1 - 0.81) = 500 \times 0.81 \times 0.19 = 76.95
\]
- Since \( 76.95 \geq 10 \), the requirement is met. Therefore, the correct choice is:
- **Option B:** Yes, because \( np_0(1 - p_0) = 76.95 \)
2. **Sample Proportion:**
- Calculate the sample proportion \(\hat{p}\):
\[
\hat{p} = \frac{390}{500} = 0.78
\]
- Enter \(\hat{p}\) as 0.78 in the answer box.
---
**Visual Aids:** No graphs or diagrams
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