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) ≥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 npo (1-P) = 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= -0.72 (Round to two decimal places as needed.) Find the P-value. P-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=0.89 versus H₁: p *0.89 n = 500, x=440, α = 0.01 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.) A. Yes, because npo (1-P) = 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= -0.72 (Round to two decimal places as needed.) Find the P-value. P-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
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![**Testing the Hypothesis Using the P-value Approach**
**Problem Statement:**
- **Hypotheses**:
- Null hypothesis (\(H_0\)): \(p = 0.89\)
- Alternative hypothesis (\(H_1\)): \(p \neq 0.89\)
- **Given values**:
- Sample size (\(n\)): 500
- Number of successes (\(x\)): 440
- Significance level (\(\alpha\)): 0.01
**Step-by-Step Verification:**
1. **Verify Requirement: \(np_0(1 - p_0) \geq 10\)**:
Calculate \(np_0(1 - p_0)\):
\[
np_0(1 - p_0) = 48.95
\]
Conclusion: Yes, because \(np_0(1 - p_0) = 48.95\).
2. **Calculate \(\hat{p}\)**:
\[
\hat{p} = \frac{x}{n} = 0.88
\]
3. **Find the Test Statistic \(z_0\)**:
\[
z_0 = -0.72
\]
(Round to two decimal places as needed.)
4. **Find the P-value**:
P-value: \(\_\_\_\)
(Round to three decimal places as needed.)
This process involves checking whether the sample meets requirements, calculating the sample proportion, determining the test statistic, and finally finding the P-value to make a decision regarding the hypothesis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac3be618-b645-4bd8-855b-808ff3fc18d4%2Fc28f81b2-0d94-4428-9e25-359ca900d0db%2Fuqx0qer_processed.png&w=3840&q=75)
Transcribed Image Text:**Testing the Hypothesis Using the P-value Approach**
**Problem Statement:**
- **Hypotheses**:
- Null hypothesis (\(H_0\)): \(p = 0.89\)
- Alternative hypothesis (\(H_1\)): \(p \neq 0.89\)
- **Given values**:
- Sample size (\(n\)): 500
- Number of successes (\(x\)): 440
- Significance level (\(\alpha\)): 0.01
**Step-by-Step Verification:**
1. **Verify Requirement: \(np_0(1 - p_0) \geq 10\)**:
Calculate \(np_0(1 - p_0)\):
\[
np_0(1 - p_0) = 48.95
\]
Conclusion: Yes, because \(np_0(1 - p_0) = 48.95\).
2. **Calculate \(\hat{p}\)**:
\[
\hat{p} = \frac{x}{n} = 0.88
\]
3. **Find the Test Statistic \(z_0\)**:
\[
z_0 = -0.72
\]
(Round to two decimal places as needed.)
4. **Find the P-value**:
P-value: \(\_\_\_\)
(Round to three decimal places as needed.)
This process involves checking whether the sample meets requirements, calculating the sample proportion, determining the test statistic, and finally finding the P-value to make a decision regarding the hypothesis.
Expert Solution
Step 1: Understanding the problem
sample size (n)=500
x=440
Null Hypothesis H0: p=0.89
Alternate Hypothesis Ha: p≠0.89
Step by step
Solved in 6 steps with 6 images
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