You obtain 255 successes in a sample of size ni 521 from the first population. You obtain 140 346 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for successes in a sample of size n2 the binomial distribution.
You obtain 255 successes in a sample of size ni 521 from the first population. You obtain 140 346 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for successes in a sample of size n2 the binomial distribution.
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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Question
![**Hypothesis Testing Overview**
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.001\):
- Null hypothesis (\(H_0\)): \(p_1 = p_2\)
- Alternative hypothesis (\(H_a\)): \(p_1 > p_2\)
**Sample Data**
- First population: 255 successes in a sample of size \(n_1 = 521\).
- Second population: 140 successes in a sample of size \(n_2 = 346\).
For this test, do not use the continuity correction. Use the normal distribution as an approximation for the binomial distribution.
**Analysis**
1. **Calculate the Test Statistic**
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
- Test statistic = [Text box for input]
2. **Determine the P-value**
What is the p-value for this sample? (Report answer accurate to four decimal places.)
- P-value = [Text box for input]
3. **Evaluate the P-value**
The p-value is...
- [ ] less than (or equal to) \(\alpha\)
- [ ] greater than \(\alpha\)
**Instructions for Completion**
- Enter the test statistic and p-value in the respective text boxes.
- Select whether the p-value is less than (or equal to) or greater than the significance level \( \alpha \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa468c45c-e596-4bb7-b4b7-93a28088c315%2F363dfc12-0c31-4fa5-a728-8e8909ba5dbf%2Fdby6tho_processed.png&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing Overview**
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.001\):
- Null hypothesis (\(H_0\)): \(p_1 = p_2\)
- Alternative hypothesis (\(H_a\)): \(p_1 > p_2\)
**Sample Data**
- First population: 255 successes in a sample of size \(n_1 = 521\).
- Second population: 140 successes in a sample of size \(n_2 = 346\).
For this test, do not use the continuity correction. Use the normal distribution as an approximation for the binomial distribution.
**Analysis**
1. **Calculate the Test Statistic**
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
- Test statistic = [Text box for input]
2. **Determine the P-value**
What is the p-value for this sample? (Report answer accurate to four decimal places.)
- P-value = [Text box for input]
3. **Evaluate the P-value**
The p-value is...
- [ ] less than (or equal to) \(\alpha\)
- [ ] greater than \(\alpha\)
**Instructions for Completion**
- Enter the test statistic and p-value in the respective text boxes.
- Select whether the p-value is less than (or equal to) or greater than the significance level \( \alpha \).
Transcribed Image Text:**Decision Based on Test Statistic**
The test statistic leads to a decision to:
- ○ Reject the null
- ○ Accept the null
- ○ Fail to reject the null
**Final Conclusion**
As such, the final conclusion is that:
- ○ There is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.
- ○ There is not sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.
- ○ The sample data support the claim that the first population proportion is greater than the second population proportion.
- ○ There is not sufficient sample evidence to support the claim that the first population proportion is greater than the second population proportion.
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