### Hypothesis Testing: Difference Between Two Means (Independent Samples)#### Problem:Do men take a different amount of time than women to get out of bed in the morning? The 51 men observed averaged 7.4 minutes to get out of bed after the alarm rang. Their standard deviation was 1.5. The 41 women observed averaged 8 minutes and their standard deviation was 1.9 minutes. What can be concluded at the \(\alpha = 0.05\) level of significance?#### Solution Steps:a. **Selection of Test:** For this study, we should use: - [ Drop-down box ] (The drop-down box should contain options like "Two-sample t-test", "Paired t-test", "One-sample t-test", and others.)b. **Formulation of Hypotheses:** The null and alternative hypotheses would be: \[ H_0: \] - [ Drop-down box ] \[ \mu_1 - \mu_2 = 0 \quad \text{(please enter a decimal)} \] \[ H_1: \] - [ Drop-down box ] \[ \mu_1 - \mu_2 \neq 0 \quad \text{(Please enter a decimal)} \]c. **Calculation of Test Statistic:** \[ \text{The test statistic} \, (t) = \] - [ Text box ] (please show your answer to 3 decimal places.)d. **Determination of P-value:** \[ \text{The p-value} = \] - [ Text box ] (Please show your answer to 4 decimal places.)e. **Conclusion:** \[ \boxed{\text{Reject} \, H_0 \, \text{if} \, p \leq \alpha } \] - [ Text box with formatted statement ]### Explanation of Variables and Calculations:- **Sample Sizes**: - Number of men (\(n_1\)) = 51 - Number of women (\(n_2\)) = 41- **Sample Means**: - Mean time for men (\(\bar{x}_1\)) =

Answered: Image /qna-images/answer/6c0966e6-67fe-4c74-a01d-01c00b85b9db.jpg

Do men take a different amount of time than women to get out of bed in the morning? The 51 men observed averaged 7.4 minutes to get out of bed after the alarm rang. Their standard deviation was 1.5. The 41 women observed averaged 8 minutes and their standard deviation was 1.9 minutes. What can be concluded at the a = 0.05 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: Select an answer Select an answer ✓ (please enter a decimal) Select an answer Select an answer H₁: Select an answer v Select an answer ✓ (Please enter a decimal) c. The test statistic ? v = (please show your answer to 3 decimal places.) d. The p-value = The pavalue is 2 x (Please show your answer to 4 decimal places.)

Do men take a different amount of time than women to get out of bed in the morning? The 51 men observed averaged 7.4 minutes to get out of bed after the alarm rang. Their standard deviation was 1.5. The 41 women observed averaged 8 minutes and their standard deviation was 1.9 minutes. What can be concluded at the a = 0.05 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: Select an answer Select an answer ✓ (please enter a decimal) Select an answer Select an answer H₁: Select an answer v Select an answer ✓ (Please enter a decimal) c. The test statistic ? v = (please show your answer to 3 decimal places.) d. The p-value = The pavalue is 2 x (Please show your answer to 4 decimal places.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 25SGR

See similar textbooks