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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
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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**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.
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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