Do the poor spend more time in the shower than the rich? The results of a survey asking poor and rich people how many minutes they spend in the shower are shown below. Poor 23 21 12 32 32 25 18 33 31 12 40 10 Rich: 20 16 3. 15 22 13 18 25 14 Assume both follow a Normal distribution. What can be concluded at the the a = 0.01 level of significance level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer vSelect an answer V Select an answer v (please enter a decimal) H: Select an answer vSelect an answer Select an answer v(Please enter a decimal) b. The test statistic ?v = (please show your answer to 3 decimal places.) c. The p-value = (Please show your answer to 4 decimal places.) d. The p-value is 2 v a e. Based on this, we should Select an answer v the null hypothesis. f. Thus, the final conclusion is that

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### 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.
Transcribed Image Text:### 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.
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