b. The null and alternative hypotheses would be: Ho: μî Select an answer H₁: με Select an answer c. The test statistic (t (please show your answer to 3 decimal places.) d. The p-value = answer to 4 decimal places) (Please show your
b. The null and alternative hypotheses would be: Ho: μî Select an answer H₁: με Select an answer c. The test statistic (t (please show your answer to 3 decimal places.) d. The p-value = answer to 4 decimal places) (Please show your
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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help with B C AND D ONLY PLEASE
![### Retirement Age Study of Small Business Owners
The average retirement age in America is 65 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.
#### Data Set:
60, 56, 63, 60, 72, 63, 64, 59, 59, 64, 68, 68
#### Question:
What can be concluded at the α = 0.05 level of significance?
### Steps to Solve:
**a. For this study, we should use:**
- T-test for a population mean
**b. The null and alternative hypotheses would be:**
\[ H_0: \mu = 65 \]
\[ H_1: \mu \ne 65 \]
**c. The test statistic:**
\[ t = \text{(please calculate and show answer to 3 decimal places)} \]
**d. The p-value:**
\[ \text{p-value} = \text{(please calculate and show answer to 4 decimal places)} \]
### Explanation:
1. **Selection of the Test**:
- One would use the T-test for a population mean because we are comparing the sample mean to the known population mean with a small sample size, and we assume the population follows a normal distribution.
2. **Formulation of Hypotheses**:
- The null hypothesis \(H_0\) states that the mean retirement age of small business owners is equal to the average retirement age in America, which is 65.
- The alternative hypothesis \(H_1\) states that the mean retirement age of small business owners is different from 65.
3. **Calculating the Test Statistic**:
- Calculate the sample mean (x̄), sample standard deviation (s), and the number of samples (n).
- Use the formula for the T-test statistic:
\[
t = \frac{x̄ - \mu}{s / \sqrt{n}}
\]
4. **Determining the p-value**:
- After obtaining the t-value, the p-value can be found using t-distribution tables or software, representing the probability of observing the test results under the null hypothesis.
This structured approach will allow us to draw a conclusion about whether small business owners retire at](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2d30e49-de0d-418d-b702-a4b3e53b4c91%2F2e46d429-9b0f-43aa-bf26-5886de921eb3%2Fybz7z5f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Retirement Age Study of Small Business Owners
The average retirement age in America is 65 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.
#### Data Set:
60, 56, 63, 60, 72, 63, 64, 59, 59, 64, 68, 68
#### Question:
What can be concluded at the α = 0.05 level of significance?
### Steps to Solve:
**a. For this study, we should use:**
- T-test for a population mean
**b. The null and alternative hypotheses would be:**
\[ H_0: \mu = 65 \]
\[ H_1: \mu \ne 65 \]
**c. The test statistic:**
\[ t = \text{(please calculate and show answer to 3 decimal places)} \]
**d. The p-value:**
\[ \text{p-value} = \text{(please calculate and show answer to 4 decimal places)} \]
### Explanation:
1. **Selection of the Test**:
- One would use the T-test for a population mean because we are comparing the sample mean to the known population mean with a small sample size, and we assume the population follows a normal distribution.
2. **Formulation of Hypotheses**:
- The null hypothesis \(H_0\) states that the mean retirement age of small business owners is equal to the average retirement age in America, which is 65.
- The alternative hypothesis \(H_1\) states that the mean retirement age of small business owners is different from 65.
3. **Calculating the Test Statistic**:
- Calculate the sample mean (x̄), sample standard deviation (s), and the number of samples (n).
- Use the formula for the T-test statistic:
\[
t = \frac{x̄ - \mu}{s / \sqrt{n}}
\]
4. **Determining the p-value**:
- After obtaining the t-value, the p-value can be found using t-distribution tables or software, representing the probability of observing the test results under the null hypothesis.
This structured approach will allow us to draw a conclusion about whether small business owners retire at
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