Do the poor spend less 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 13 21 13 39 8 22 30 36 19 33 Rich: 55 29 34 15 33 40 39 45 26 32 55 49 27 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: ) (please enter a decimal) | (Please enter a decimal) Ho: Select an answer Select an answer Select an answer H1: Select an answer Select an answer Select an answer b. The test statistic (please show your answer to 3 decimal places.) c. The p-value - d. The p-value is ? a e. Based on this, we should Select an answer f. Thus, the final conclusion is that.. |(Please show your answer to 4 decimal places.) ) the null hypothesis. O The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean time in the shower for the poor is less than the population mean time in the shower for the rich. The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the mean time in the shower for the ten poor people that were surveyed is less than the mean time in the shower for the thirteen rich people that were surveyed. The results are statistically insignificant at a = 0.01, so there is statistically significant evidence to conclude that the population mean time in the shower for the poor is equal to the population mean time in the shower for the rich. O The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the population mean time in the shower for the poor is less than the population mean time in the shower for the rich.
Do the poor spend less 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 13 21 13 39 8 22 30 36 19 33 Rich: 55 29 34 15 33 40 39 45 26 32 55 49 27 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: ) (please enter a decimal) | (Please enter a decimal) Ho: Select an answer Select an answer Select an answer H1: Select an answer Select an answer Select an answer b. The test statistic (please show your answer to 3 decimal places.) c. The p-value - d. The p-value is ? a e. Based on this, we should Select an answer f. Thus, the final conclusion is that.. |(Please show your answer to 4 decimal places.) ) the null hypothesis. O The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean time in the shower for the poor is less than the population mean time in the shower for the rich. The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the mean time in the shower for the ten poor people that were surveyed is less than the mean time in the shower for the thirteen rich people that were surveyed. The results are statistically insignificant at a = 0.01, so there is statistically significant evidence to conclude that the population mean time in the shower for the poor is equal to the population mean time in the shower for the rich. O The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the population mean time in the shower for the poor is less than the population mean time in the shower for the rich.
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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Transcribed Image Text:**Survey Analysis on Shower Duration**
In a study examining whether socio-economic status affects shower duration, a survey was conducted where poor and rich individuals reported the number of minutes they spend in the shower. The results are tabulated below:
- **Poor:**
- Minutes: 13, 21, 13, 39, 8, 22, 30, 36, 19, 33
- **Rich:**
- Minutes: 55, 29, 34, 15, 33, 40, 39, 45, 26, 32, 55, 49, 27
### Hypothesis Testing
Assuming a normal distribution, the goal is to determine if there is a significant difference between the two groups using a significance level (\(\alpha\)) of 0.01.
#### Steps to Conclusion
**a. Formation of Hypotheses**
- **Null Hypothesis (\(H_0\))**: This typically states there is no effect or no difference.
- **Alternative Hypothesis (\(H_1\))**: This states there is an effect, or there is a difference.
**b. Test Statistic Calculation**
- Compute the test statistic using the appropriate formula, rounding your answer to three decimal places.
**c. p-value Calculation**
- Determine the p-value from the statistical test and round to four decimal places.
**d. Comparison with Alpha**
- Compare the p-value to the significance level (\(\alpha\)) of 0.01 to determine the strength of evidence against the null hypothesis.
**e. Decision Rule**
- Based on the comparison, decide whether to reject or fail to reject the null hypothesis.
**f. Final Conclusion**
- The options provided guide the researcher to conclude whether the observed difference is statistically significant:
- **Option 1**: No significant difference.
- **Option 2**: Significant difference, more time spent in the shower by the rich.
- **Option 3**: Statistically significant, equal average shower times.
- **Option 4**: Significant difference, more time spent in the shower by the poor.
This structured approach allows students to understand how hypothesis testing is applied in real-world situations, emphasizing critical statistical thinking.
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