### Analysis of Shower Time Between Different Income Groups#### Survey Results:A survey investigated whether economically disadvantaged people (referred to as "poor") spend more time in the shower compared to affluent people ("rich"). Below are the recorded shower times (in minutes) for each group:- **Poor**: 23, 21, 8, 19, 32, 35, 18, 33, 31, 12, 40, 10- **Rich**: 20, 15, 9, 19, 13, 18, 25, 14, 3#### Statistical Analysis:Both groups are assumed to follow a normal distribution. The analysis aims to determine, at a significance level of \( \alpha = 0.01 \), whether the average shower time for the poor is greater than that for the rich.1. **Hypotheses:** - Null Hypothesis (\( H_0 \)): The mean shower time for the poor is equal to or less than that for the rich. - Alternative Hypothesis (\( H_1 \)): The mean shower time for the poor is greater than that for the rich.2. **Test Statistic Calculation:** - The test statistic is calculated and should be displayed to three decimal places.3. **p-value:** - Calculated and displayed to four decimal places.4. **Comparison:** - The p-value is compared to \( \alpha \) to determine whether to reject the null hypothesis.5. **Conclusion Options:** - If results are statistically insignificant at \( \alpha = 0.01 \), there is no significant evidence to reject the null hypothesis. - If results are statistically significant, conclusion statements determine whether there is sufficient evidence to support that the poor spend more time in the shower than the rich.These statistical steps guide the analysis and help in drawing a conclusion about the differences in average showering time between the two groups, while ensuring consideration of statistical significance and hypothesis testing procedures.

The data shows the results of a survey asking poor and rich people how many minutes they spend in the shower.The population standard deviation is not known, and both samples follows normal distribution indicating that the t-test for two independent samples is used for this study. Therefore, the t-test for two independent samples is used for this study.a. Let μ1 be the true average time spend in the shower of poor people, and μ2 be the true average time spend in the shower of rich people. the claim is to check whether the poor spend more time in the shower than the rich or not. The hypothesis is, Null hypothesis: H0:μ1≤μ2 Alternative hypothesis: H1:μ1>μ2b. The test statistic is obtained by using the EXCEL data analysis procedure as follows: Enter the data. Select Data > Data Analysis >t-Test: Two-Sample Assuming Unequal Variances> OK. Enter Variable 1 Range as A1:A14. Enter Variable 2 Range as B1:B13. Enter Hypothesized Mean Difference as 0. Mark Labels in First Row. Enter Alpha as 0.01. Click OK. The output is, From the output, the test statistic is 2.600. Therefore, the test statistic t=2.600.c. From the output, the p-value for one tailed area is 0.0082. Therefore, the p-value is 0.0082.d, e, and f. Decision rule: If p-value≤α, then reject the null hypothesis. Conclusion: The p-value (0.0082) is less than the level of significance (0.01). Based on decision rule, reject the null hypothesis. Thus, the results are statistically significant at α=0.01, so there is sufficient evidence to conclude that the population mean time in the shower for the poor is more than the population mean time in the shower for the rich.