### Statistical Analysis Example: Determining Differences in Time Taken to Get Out of Bed#### Problem Statement:Do men take a different amount of time than women to get out of bed in the morning? The 54 men observed averaged 4.3 minutes to get out of bed after the alarm rang. Their standard deviation was 1.4. The 59 women observed averaged 5 minutes and their standard deviation was 2.8 minutes. What can be concluded at the $\alpha = 0.01$ level of significance?#### Solution Steps:1. **Select the Appropriate Test:** For this study, we should use a **t-test for the difference between two independent population means**.2. **Formulate Hypotheses:** - Null hypothesis ($H_0$): $\mu_1 = \mu_2$ - Alternative hypothesis ($H_1$): $\mu_1 \ne \mu_2$3. **Compute the Test Statistic:** - Let $t = $ (This value should be calculated using the appropriate statistical formula. Please show your answer to 3 decimal places.) 4. **Calculate the p-value:** - The p-value = (Please show your answer to 4 decimal places.)5. **Compare the p-value with $\alpha$:** - The p-value is > $\alpha$ 6. **Conclusion:** - Based on this statistic, we should **fail to reject** the null hypothesis.### Explanation of Terms and Concepts:- **Null Hypothesis ($H_0$)**: This assumes that there is no difference in the average time taken by men and women to get out of bed. In this context, $\mu_1$ and $\mu_2$ represent the mean times for men and women, respectively. - **Alternative Hypothesis ($H_1$)**: This posits that there is a difference in the means, indicating that men and women take different times to get out of bed.- **Test Statistic (t-value)**: This is a value calculated from the sample data used to determine whether to reject the null hypothesis. - **p-value**: This indicates the probability of obtaining test results at least as extreme as the observed results, under the assumption that the null hypothesis is true.- **Level of Sign

Solution: Given information: n1= 54 Sample size of men n2= 59 Sample size of women x1= 4.3 Sample…

Answered: Do men take a different amount of time…

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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