### Hypothesis Testing Using the t-Distribution Use the t-distribution and the sample results to complete the test of the hypothesis \(15\% \) significance level. Assume the results come from a random sample, and the sample size is small. #### Step-by-Step Instructions: 1. **Test Hypotheses:** - Null Hypothesis (\(H_0\)): \(\mu = 15\) - Alternative Hypothesis (\(H_a\)): \(\mu > 15\) Given sample results: \[ \bar{x} = 17.2, s = 6.4, \text{ with } n = 40 \] 2. **Calculate the Test Statistic and p-value:** - Use the formula for the test statistic: \[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \] - Calculate the p-value using the calculated test statistic and the t-distribution table or software. 3. **Round your answers:** - Round the test statistic to two decimal places. - Round the p-value to three decimal places. 4. **Make a conclusion:** - Compare the p-value to the significance level (0.05): - If p-value \(\leq\) 0.05, reject the null hypothesis (\(H_0\)). - If p-value > 0.05, do not reject the null hypothesis (\(H_0\)). #### Input Fields: - **Test Statistic:** - Input box for the calculated test statistic rounded to two decimal places. - **p-value:** - Input box for the calculated p-value rounded to three decimal places. #### Conclusion Section: - **What is the conclusion?** - **Options:** - Reject \(H_0\) - Do not reject \(H_0\) Use the above steps and information to conduct the hypothesis test effectively.
### Hypothesis Testing Using the t-Distribution Use the t-distribution and the sample results to complete the test of the hypothesis \(15\% \) significance level. Assume the results come from a random sample, and the sample size is small. #### Step-by-Step Instructions: 1. **Test Hypotheses:** - Null Hypothesis (\(H_0\)): \(\mu = 15\) - Alternative Hypothesis (\(H_a\)): \(\mu > 15\) Given sample results: \[ \bar{x} = 17.2, s = 6.4, \text{ with } n = 40 \] 2. **Calculate the Test Statistic and p-value:** - Use the formula for the test statistic: \[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \] - Calculate the p-value using the calculated test statistic and the t-distribution table or software. 3. **Round your answers:** - Round the test statistic to two decimal places. - Round the p-value to three decimal places. 4. **Make a conclusion:** - Compare the p-value to the significance level (0.05): - If p-value \(\leq\) 0.05, reject the null hypothesis (\(H_0\)). - If p-value > 0.05, do not reject the null hypothesis (\(H_0\)). #### Input Fields: - **Test Statistic:** - Input box for the calculated test statistic rounded to two decimal places. - **p-value:** - Input box for the calculated p-value rounded to three decimal places. #### Conclusion Section: - **What is the conclusion?** - **Options:** - Reject \(H_0\) - Do not reject \(H_0\) Use the above steps and information to conduct the hypothesis test effectively.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Hypothesis Testing Using the t-Distribution
Use the t-distribution and the sample results to complete the test of the hypothesis \(15\% \) significance level. Assume the results come from a random sample, and the sample size is small.
#### Step-by-Step Instructions:
1. **Test Hypotheses:**
- Null Hypothesis (\(H_0\)): \(\mu = 15\)
- Alternative Hypothesis (\(H_a\)): \(\mu > 15\)
Given sample results:
\[
\bar{x} = 17.2, s = 6.4, \text{ with } n = 40
\]
2. **Calculate the Test Statistic and p-value:**
- Use the formula for the test statistic:
\[
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
\]
- Calculate the p-value using the calculated test statistic and the t-distribution table or software.
3. **Round your answers:**
- Round the test statistic to two decimal places.
- Round the p-value to three decimal places.
4. **Make a conclusion:**
- Compare the p-value to the significance level (0.05):
- If p-value \(\leq\) 0.05, reject the null hypothesis (\(H_0\)).
- If p-value > 0.05, do not reject the null hypothesis (\(H_0\)).
#### Input Fields:
- **Test Statistic:**
- Input box for the calculated test statistic rounded to two decimal places.
- **p-value:**
- Input box for the calculated p-value rounded to three decimal places.
#### Conclusion Section:
- **What is the conclusion?**
- **Options:**
- Reject \(H_0\)
- Do not reject \(H_0\)
Use the above steps and information to conduct the hypothesis test effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F915c192e-d8ba-4859-b60e-5e514228af12%2Ffb104fc6-abc3-4ae3-bae2-c0c6a71a36f6%2F3e2ha3.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Using the t-Distribution
Use the t-distribution and the sample results to complete the test of the hypothesis \(15\% \) significance level. Assume the results come from a random sample, and the sample size is small.
#### Step-by-Step Instructions:
1. **Test Hypotheses:**
- Null Hypothesis (\(H_0\)): \(\mu = 15\)
- Alternative Hypothesis (\(H_a\)): \(\mu > 15\)
Given sample results:
\[
\bar{x} = 17.2, s = 6.4, \text{ with } n = 40
\]
2. **Calculate the Test Statistic and p-value:**
- Use the formula for the test statistic:
\[
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
\]
- Calculate the p-value using the calculated test statistic and the t-distribution table or software.
3. **Round your answers:**
- Round the test statistic to two decimal places.
- Round the p-value to three decimal places.
4. **Make a conclusion:**
- Compare the p-value to the significance level (0.05):
- If p-value \(\leq\) 0.05, reject the null hypothesis (\(H_0\)).
- If p-value > 0.05, do not reject the null hypothesis (\(H_0\)).
#### Input Fields:
- **Test Statistic:**
- Input box for the calculated test statistic rounded to two decimal places.
- **p-value:**
- Input box for the calculated p-value rounded to three decimal places.
#### Conclusion Section:
- **What is the conclusion?**
- **Options:**
- Reject \(H_0\)
- Do not reject \(H_0\)
Use the above steps and information to conduct the hypothesis test effectively.
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