The average retirement age in America is 63 years old. Do small business owners retire at a different average age? The data below shows the results of a survey of small business owners who have recently retired. Assume that the distribution of the population is normal. 72, 70, 67, 70, 65, 64, 59, 57, 74, 68, 63, 66, 68, 57 What can be concluded at the the a = 0.01 level of significance level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: ? Select an answer î H₁: ? î Select an answer c. The test statistic ? = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? Εα f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population mean is not significantly different from 63 at a = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 63. The data suggest the population mean retirement age for small business owners is not significantly different from 63 at a = 0.01, so there is insufficient evidence to conclude that the population mean retirement age for small business owners is different from 63. O The data suggest the populaton mean is significantly different from 63 at a = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is different from 63.
The average retirement age in America is 63 years old. Do small business owners retire at a different average age? The data below shows the results of a survey of small business owners who have recently retired. Assume that the distribution of the population is normal. 72, 70, 67, 70, 65, 64, 59, 57, 74, 68, 63, 66, 68, 57 What can be concluded at the the a = 0.01 level of significance level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: ? Select an answer î H₁: ? î Select an answer c. The test statistic ? = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? Εα f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population mean is not significantly different from 63 at a = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 63. The data suggest the population mean retirement age for small business owners is not significantly different from 63 at a = 0.01, so there is insufficient evidence to conclude that the population mean retirement age for small business owners is different from 63. O The data suggest the populaton mean is significantly different from 63 at a = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is different from 63.
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:**Investigating the Retirement Age for Small Business Owners**
**Research Question:**
The average retirement age in America is 63 years old. Do small business owners retire at a different average age? The data below shows the results of a survey of small business owners who have recently retired. Assume that the distribution of the population is normal.
**Survey Data:**
72, 70, 67, 70, 65, 64, 59, 57, 74, 68, 63, 66, 68, 57
**Objective:**
Determine if the average retirement age for small business owners is significantly different from the national average of 63 using a significance level of α = 0.01.
### Steps for Analysis:
1. **Select the Appropriate Test:**
For this study, we should use a
- **t-test for a population mean**
2. **Formulate Hypotheses:**
- **Null Hypothesis (H₀):** The average retirement age for small business owners is equal to 63.
- **Alternative Hypothesis (H₁):** The average retirement age for small business owners is not equal to 63.
3. **Compute the Test Statistic:**
- Using the provided data, calculate the test statistic (t-value) to 3 decimal places.
4. **Find the p-value:**
- Calculate the p-value and report it to 4 decimal places.
5. **Compare the p-value with α:**
- Determine whether the p-value is less than or greater than α (0.01).
6. **Make a Decision:**
- Based on the comparison, decide whether to reject or fail to reject the null hypothesis.
7. **Draw a Conclusion:**
- Conclude if there is sufficient evidence to suggest that the average retirement age for small business owners is different from 63 years.
### Final Conclusion Options:
\( \) The data suggest the population mean is not significantly different from 63 at α = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 63.
\( \) The data suggest the population mean retirement age for small business owners is not significantly different from 63 at α = 0.01, so there is insufficient evidence to conclude that the population mean retirement age for small business owners is different from 63.
\( \)
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