The average retirement age in America is 65 years old. Do small business owners retire at an older 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. 58, 62, 73, 77, 61, 74, 75, 62, 70, 69, 64, 76, 70, 64, 70, 64 What can be concluded at the the a = 0.05 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: Но: μν 65 H1: 65 c. The test statistic [ t 2.504 (please show your answer to 3 decimal places.) d. The p-value = 0.0122 X (Please show your answer to 4 decimal places.) II

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Just part C and D (the ones circled in red) 

### Retirement Age Analysis for Small Business Owners

**Objective:**  
Determine if small business owners retire at an older average age compared to the general American population, whose average retirement age is 65 years.

#### Data Collected:
The following retirement ages of small business owners were surveyed:  
58, 62, 73, 77, 61, 74, 75, 62, 70, 69, 64, 76, 70, 64

#### Hypothesis Testing:
- **Significance Level:** \(\alpha = 0.05\)

#### a. Statistical Test Used:
To assess the hypothesis, a **t-test for a population mean** is appropriate due to the assumption of normal distribution.

#### b. Null and Alternative Hypotheses:
- **Null Hypothesis (\(H_0\)):** \(\mu = 65\)
  - The average retirement age of small business owners is 65.
  
- **Alternative Hypothesis (\(H_1\)):** \(\mu > 65\)
  - The average retirement age of small business owners is greater than 65.

#### c. Test Statistic:
- **Calculated t-value:** \(t = 2.504\)

#### d. P-value:
- **P-value:** \(0.0122\)

**Conclusion:**  
The p-value (0.0122) is less than the significance level (0.05), suggesting that there is statistically significant evidence to support the claim that small business owners retire at an older age than the general population average of 65 years.
Transcribed Image Text:### Retirement Age Analysis for Small Business Owners **Objective:** Determine if small business owners retire at an older average age compared to the general American population, whose average retirement age is 65 years. #### Data Collected: The following retirement ages of small business owners were surveyed: 58, 62, 73, 77, 61, 74, 75, 62, 70, 69, 64, 76, 70, 64 #### Hypothesis Testing: - **Significance Level:** \(\alpha = 0.05\) #### a. Statistical Test Used: To assess the hypothesis, a **t-test for a population mean** is appropriate due to the assumption of normal distribution. #### b. Null and Alternative Hypotheses: - **Null Hypothesis (\(H_0\)):** \(\mu = 65\) - The average retirement age of small business owners is 65. - **Alternative Hypothesis (\(H_1\)):** \(\mu > 65\) - The average retirement age of small business owners is greater than 65. #### c. Test Statistic: - **Calculated t-value:** \(t = 2.504\) #### d. P-value: - **P-value:** \(0.0122\) **Conclusion:** The p-value (0.0122) is less than the significance level (0.05), suggesting that there is statistically significant evidence to support the claim that small business owners retire at an older age than the general population average of 65 years.
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