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

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Only parts c and d

**Title: Statistical Analysis of Retirement Age Among Small Business Owners**

**Introduction**
The average retirement age in America is 65 years. This study investigates whether small business owners retire later than the average. The data presented below is from a survey of small business owners who have recently retired, assuming the population distribution is normal.

**Data**
- Retirement ages: 58, 62, 73, 77, 61, 74, 75, 62, 70, 69, 64, 76, 70, 64, 70, 64

**Objective**
To determine, at a significance level of α = 0.05, whether small business owners retire at an older age than the general population.

**Methodology**

a. **Statistical Test**
   - Utilize a t-test for a population mean.

b. **Hypotheses**
   - Null Hypothesis (\(H_0\)): \( \mu = 65 \)
   - Alternative Hypothesis (\(H_1\)): \( \mu > 65 \)

**Analysis**

c. **Test Statistic Calculation**
   - Calculate the test statistic \( t \) (provide your answer to 3 decimal places).

d. **P-Value Calculation**
   - Determine the p-value (provide your answer to 4 decimal places).

**Conclusion**
Through the statistical analysis using the t-test for a population mean, we aim to conclude whether the observed data provides sufficient evidence to support that small business owners retire at a later age than the average American retirement age.
Transcribed Image Text:**Title: Statistical Analysis of Retirement Age Among Small Business Owners** **Introduction** The average retirement age in America is 65 years. This study investigates whether small business owners retire later than the average. The data presented below is from a survey of small business owners who have recently retired, assuming the population distribution is normal. **Data** - Retirement ages: 58, 62, 73, 77, 61, 74, 75, 62, 70, 69, 64, 76, 70, 64, 70, 64 **Objective** To determine, at a significance level of α = 0.05, whether small business owners retire at an older age than the general population. **Methodology** a. **Statistical Test** - Utilize a t-test for a population mean. b. **Hypotheses** - Null Hypothesis (\(H_0\)): \( \mu = 65 \) - Alternative Hypothesis (\(H_1\)): \( \mu > 65 \) **Analysis** c. **Test Statistic Calculation** - Calculate the test statistic \( t \) (provide your answer to 3 decimal places). d. **P-Value Calculation** - Determine the p-value (provide your answer to 4 decimal places). **Conclusion** Through the statistical analysis using the t-test for a population mean, we aim to conclude whether the observed data provides sufficient evidence to support that small business owners retire at a later age than the average American retirement age.
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