Hypothesis Test for the Difference in Two Proportions You wish to test the following claim (Ha) at a significance level of a = 0.02. Ho:P1 = p2 Ha:pi > p2 You obtain 79.5% successes in a sample of size n1 = 541 from the first population. You obtain 74.3% successes in a sample of size n2 = 490 from the second population. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =
Hypothesis Test for the Difference in Two Proportions You wish to test the following claim (Ha) at a significance level of a = 0.02. Ho:P1 = p2 Ha:pi > p2 You obtain 79.5% successes in a sample of size n1 = 541 from the first population. You obtain 74.3% successes in a sample of size n2 = 490 from the second population. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =
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 Test for the Difference in Two Proportions**
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.02\).
\[
H_0: p_1 = p_2 \\
H_a: p_1 > p_2
\]
You obtain 79.5% successes in a sample of size \(n_1 = 541\) from the first population. You obtain 74.3% successes in a sample of size \(n_2 = 490\) from the second population.
**What is the test statistic for this sample?** (Report answer accurate to three decimal places.)
Test statistic = [ ]
**What is the p-value for this sample?** (Report answer accurate to four decimal places.)
p-value = [ ]
The p-value is...
- [ ] less than (or equal to) \(\alpha\)
- [ ] greater than \(\alpha\)
This test statistic leads to a decision to...
- [ ] reject the null
- [ ] accept the null
- [ ] fail to reject the null
**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.
---
This section outlines a hypothesis test for comparing two population proportions. You assess whether the first population proportion is significantly greater than the second at a specified level of significance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c34f4d9-e916-4e51-bbe7-df3a13f5e09c%2F7276542e-ce2e-4525-bd5c-ccca49bba271%2Fwiw0skj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Test for the Difference in Two Proportions**
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.02\).
\[
H_0: p_1 = p_2 \\
H_a: p_1 > p_2
\]
You obtain 79.5% successes in a sample of size \(n_1 = 541\) from the first population. You obtain 74.3% successes in a sample of size \(n_2 = 490\) from the second population.
**What is the test statistic for this sample?** (Report answer accurate to three decimal places.)
Test statistic = [ ]
**What is the p-value for this sample?** (Report answer accurate to four decimal places.)
p-value = [ ]
The p-value is...
- [ ] less than (or equal to) \(\alpha\)
- [ ] greater than \(\alpha\)
This test statistic leads to a decision to...
- [ ] reject the null
- [ ] accept the null
- [ ] fail to reject the null
**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.
---
This section outlines a hypothesis test for comparing two population proportions. You assess whether the first population proportion is significantly greater than the second at a specified level of significance.
Expert Solution

Step 1
Hypothesis test :
The null and alternative hypothesis is
Ho : p1 = p2
Ha : p1 > p2
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