MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Members of fraternities and sororities are required to volunteer for community service. Do fraternity brothers work an equal number of volunteer hours on average compared to sorority sisters? The data below show the number of volunteer hours worked for thirteen randomly selected fraternity brothers and eleven randomly selected sorority sisters. - **Brothers:** 13, 14, 8, 4, 3, 4, 5, 12, 7, 14, 8 - **Sisters:** 15, 18, 4, 13, 5, 7, 19, 12, 19, 14, 7 Assume both follow a Normal distribution. What can be concluded at the α = 0.05 level of significance? For this study, we use a **t-test for the difference between two independent population means**. ### a. The null and alternative hypotheses would be: - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 \neq \mu_2 \) ### b. The test statistic - Test statistic \( t = -2.813 \) ### c. The p-value - p-value = 0.0101 ### d. The p-value is \( \leq \alpha \) ### e. Based on this, we should: - **Reject** the null hypothesis. ### f. Thus, the final conclusion is that: - The results are statistically significant at \( \alpha = 0.05 \), so there is sufficient evidence to conclude that the population mean volunteer hours for fraternity brothers is not the same as the population mean volunteer work hours for sorority sisters.
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Transcribed Image Text:Members of fraternities and sororities are required to volunteer for community service. Do fraternity brothers work an equal number of volunteer hours on average compared to sorority sisters? The data below show the number of volunteer hours worked for thirteen randomly selected fraternity brothers and eleven randomly selected sorority sisters. - **Brothers:** 13, 14, 8, 4, 3, 4, 5, 12, 7, 14, 8 - **Sisters:** 15, 18, 4, 13, 5, 7, 19, 12, 19, 14, 7 Assume both follow a Normal distribution. What can be concluded at the α = 0.05 level of significance? For this study, we use a **t-test for the difference between two independent population means**. ### a. The null and alternative hypotheses would be: - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 \neq \mu_2 \) ### b. The test statistic - Test statistic \( t = -2.813 \) ### c. The p-value - p-value = 0.0101 ### d. The p-value is \( \leq \alpha \) ### e. Based on this, we should: - **Reject** the null hypothesis. ### f. Thus, the final conclusion is that: - The results are statistically significant at \( \alpha = 0.05 \), so there is sufficient evidence to conclude that the population mean volunteer hours for fraternity brothers is not the same as the population mean volunteer work hours for sorority sisters.
Expert Solution
Check Mark
Step 1: We have given that

Test statistic t = -2.813

Null and alternate hypothesis

H0:μ1=μ2

H1:μ1≠μ2


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