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Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given for Friday the 6th and Friday the 13th in the same month. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with median equal to zero at a significance level of a = 0.05. Fri. 6th 9 8 7 13 6 D 11 6 6 Fri. 13th 10 9 12 12 Click to view a table of critical values for the Wilcoxon signed-ranks test. First define the null and alternative hypotheses. Ho: The population of differences has a median equal to 0. H₁: The population of differences has a median not equal to 0. Calculate the test statistic. T= Calculate the critical value. The critical value is What is the conclusion for this hypothesis test? O A. Reject Ho. There is insufficient evidence to warrant rejection of the claim of no difference. O B. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim of no difference. O C. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim of no difference. OD. Reject Ho. There is sufficient evidence to warrant rejection of the claim of no difference.

Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given for Friday the 6th and Friday the 13th in the same month. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with median equal to zero at a significance level of a = 0.05. Fri. 6th 9 8 7 13 6 D 11 6 6 Fri. 13th 10 9 12 12 Click to view a table of critical values for the Wilcoxon signed-ranks test. First define the null and alternative hypotheses. Ho: The population of differences has a median equal to 0. H₁: The population of differences has a median not equal to 0. Calculate the test statistic. T= Calculate the critical value. The critical value is What is the conclusion for this hypothesis test? O A. Reject Ho. There is insufficient evidence to warrant rejection of the claim of no difference. O B. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim of no difference. O C. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim of no difference. OD. Reject Ho. There is sufficient evidence to warrant rejection of the claim of no difference.

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
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### Wilcoxon Signed-Ranks Test for Comparing Hospital Admissions on Different Days Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given for Friday the 6th and Friday the 13th in the same month. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with median equal to zero at a significance level of \(\alpha = 0.05\). #### Data | Date | Admissions | |------|-------------| | Fri. 6th | 9, 8, 7, 13, 11, 6 | | Fri. 13th | 10, 9, 12, 6, 6, 12 | #### Statistical Test Click to view a table of critical values for the Wilcoxon signed-ranks test. - **Null Hypothesis (\(H_0\))**: The population of differences has a median equal to 0. - **Alternative Hypothesis (\(H_1\))**: The population of differences has a median not equal to 0. #### Steps for Calculation 1. **Calculate the Test Statistic (T)** \[ T = \_\_\_ \] 2. **Calculate the Critical Value** \[ The\ critical\ value\ is\ \_\_\_ \] #### Conclusion for this Hypothesis Test What is the conclusion for this hypothesis test? - **A.** Reject \(H_0\). There is insufficient evidence to warrant rejection of the claim of no difference. - **B.** Fail to reject \(H_0\). There is sufficient evidence to warrant rejection of the claim of no difference. - **C.** Fail to reject \(H_0\). There is insufficient evidence to warrant rejection of the claim of no difference. - **D.** Reject \(H_0\). There is sufficient evidence to warrant rejection of the claim of no difference.
Transcribed Image Text:### Wilcoxon Signed-Ranks Test for Comparing Hospital Admissions on Different Days Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given for Friday the 6th and Friday the 13th in the same month. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with median equal to zero at a significance level of \(\alpha = 0.05\). #### Data | Date | Admissions | |------|-------------| | Fri. 6th | 9, 8, 7, 13, 11, 6 | | Fri. 13th | 10, 9, 12, 6, 6, 12 | #### Statistical Test Click to view a table of critical values for the Wilcoxon signed-ranks test. - **Null Hypothesis (\(H_0\))**: The population of differences has a median equal to 0. - **Alternative Hypothesis (\(H_1\))**: The population of differences has a median not equal to 0. #### Steps for Calculation 1. **Calculate the Test Statistic (T)** \[ T = \_\_\_ \] 2. **Calculate the Critical Value** \[ The\ critical\ value\ is\ \_\_\_ \] #### Conclusion for this Hypothesis Test What is the conclusion for this hypothesis test? - **A.** Reject \(H_0\). There is insufficient evidence to warrant rejection of the claim of no difference. - **B.** Fail to reject \(H_0\). There is sufficient evidence to warrant rejection of the claim of no difference. - **C.** Fail to reject \(H_0\). There is insufficient evidence to warrant rejection of the claim of no difference. - **D.** Reject \(H_0\). There is sufficient evidence to warrant rejection of the claim of no difference.
### Critical Values of T for the Wilcoxon Signed-Ranks Test The table below displays the critical values of \( T \) for the Wilcoxon Signed-Ranks Test, which is a non-parametric statistical hypothesis test used to compare paired samples to assess whether their population mean ranks differ. The table includes critical values for various sample sizes \( n \), under different significance levels \( \alpha \), for both one-tailed and two-tailed tests. #### Table: Critical Values of \( T \) for the Wilcoxon Signed-Ranks Test | \( n \) | \(\alpha = 0.005\) <br> (one tail) <br> \(0.01\) (two tails) | \(\alpha = 0.01\) <br> (one tail) <br> \(0.02\) (two tails) | \(\alpha = 0.025\) <br> (one tail) <br> \(0.05\) (two tails) | \(\alpha = 0.05\) <br> (one tail) <br> \(0.10\) (two tails) | \( n \) | |------|-------------------------------------------------|-------------------------------------------------|-------------------------------------------------|------------------------------------------------|-------| | 5 | * | * | * | 1 | 5 | | 6 | * | * | 1 | 2 | 6 | | 7 | * | 0 | 2 | 4 | 7 | | 8 | 0 | 2 | 4 | 6 | 8 | | 9 | 2 | 3 | 6 | 8 | 9 | | 10 | 3 | 5 | 8 | 11 | 10 | | 11 | 5 | 7 | 11 | 14 | 11 | | 12 | 7 | 10 | 14 | 17 | 12 | | 13 | 10 | 13 | 17 | 21 | 13 | | 14 | 13 | 16 | 21 | 26
Transcribed Image Text:### Critical Values of T for the Wilcoxon Signed-Ranks Test The table below displays the critical values of \( T \) for the Wilcoxon Signed-Ranks Test, which is a non-parametric statistical hypothesis test used to compare paired samples to assess whether their population mean ranks differ. The table includes critical values for various sample sizes \( n \), under different significance levels \( \alpha \), for both one-tailed and two-tailed tests. #### Table: Critical Values of \( T \) for the Wilcoxon Signed-Ranks Test | \( n \) | \(\alpha = 0.005\) <br> (one tail) <br> \(0.01\) (two tails) | \(\alpha = 0.01\) <br> (one tail) <br> \(0.02\) (two tails) | \(\alpha = 0.025\) <br> (one tail) <br> \(0.05\) (two tails) | \(\alpha = 0.05\) <br> (one tail) <br> \(0.10\) (two tails) | \( n \) | |------|-------------------------------------------------|-------------------------------------------------|-------------------------------------------------|------------------------------------------------|-------| | 5 | * | * | * | 1 | 5 | | 6 | * | * | 1 | 2 | 6 | | 7 | * | 0 | 2 | 4 | 7 | | 8 | 0 | 2 | 4 | 6 | 8 | | 9 | 2 | 3 | 6 | 8 | 9 | | 10 | 3 | 5 | 8 | 11 | 10 | | 11 | 5 | 7 | 11 | 14 | 11 | | 12 | 7 | 10 | 14 | 17 | 12 | | 13 | 10 | 13 | 17 | 21 | 13 | | 14 | 13 | 16 | 21 | 26
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