### Hypothesis Testing Using t-Distribution **Problem Statement:** Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples and that the sample sizes are small. Also, assume the underlying distributions are relatively normal. **Given Hypotheses:** - Null Hypothesis (H₀): μ₁ = μ₂ - Alternative Hypothesis (H₁): μ₁ ≠ μ₂ **Sample Results:** - Mean of sample 1 (x₁̄): 15.3 - Standard deviation of sample 1 (s₁): 11.6 - Sample size of sample 1 (n₁): 100 - Mean of sample 2 (x₂̄): 18.4 - Standard deviation of sample 2 (s₂): 14.3 - Sample size of sample 2 (n₂): 80 **(a) Calculate the Test Statistic and p-value:** Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. **Text Fields**: - Test Statistic: [Input Field] - p-value: [Input Field] **(b) Conclusion of the Test:** - **Radio Button Options:** - Reject H₀ - Do not reject H₀ **Question:** What is the conclusion of the test? Test at a 10% significance level. ### Explanation: This problem involves performing a hypothesis test for the difference in means using the t-distribution due to small sample sizes. The test statistic is calculated using the given sample means, standard deviations, and sizes. The p-value is then determined for the calculated test statistic, and the decision to reject or not reject the null hypothesis is made based on the p-value and the significance level.
### Hypothesis Testing Using t-Distribution **Problem Statement:** Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples and that the sample sizes are small. Also, assume the underlying distributions are relatively normal. **Given Hypotheses:** - Null Hypothesis (H₀): μ₁ = μ₂ - Alternative Hypothesis (H₁): μ₁ ≠ μ₂ **Sample Results:** - Mean of sample 1 (x₁̄): 15.3 - Standard deviation of sample 1 (s₁): 11.6 - Sample size of sample 1 (n₁): 100 - Mean of sample 2 (x₂̄): 18.4 - Standard deviation of sample 2 (s₂): 14.3 - Sample size of sample 2 (n₂): 80 **(a) Calculate the Test Statistic and p-value:** Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. **Text Fields**: - Test Statistic: [Input Field] - p-value: [Input Field] **(b) Conclusion of the Test:** - **Radio Button Options:** - Reject H₀ - Do not reject H₀ **Question:** What is the conclusion of the test? Test at a 10% significance level. ### Explanation: This problem involves performing a hypothesis test for the difference in means using the t-distribution due to small sample sizes. The test statistic is calculated using the given sample means, standard deviations, and sizes. The p-value is then determined for the calculated test statistic, and the decision to reject or not reject the null hypothesis is made based on the p-value and the significance level.
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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![### Hypothesis Testing Using t-Distribution
**Problem Statement:**
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples and that the sample sizes are small. Also, assume the underlying distributions are relatively normal.
**Given Hypotheses:**
- Null Hypothesis (H₀): μ₁ = μ₂
- Alternative Hypothesis (H₁): μ₁ ≠ μ₂
**Sample Results:**
- Mean of sample 1 (x₁̄): 15.3
- Standard deviation of sample 1 (s₁): 11.6
- Sample size of sample 1 (n₁): 100
- Mean of sample 2 (x₂̄): 18.4
- Standard deviation of sample 2 (s₂): 14.3
- Sample size of sample 2 (n₂): 80
**(a) Calculate the Test Statistic and p-value:**
Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.
**Text Fields**:
- Test Statistic: [Input Field]
- p-value: [Input Field]
**(b) Conclusion of the Test:**
- **Radio Button Options:**
- Reject H₀
- Do not reject H₀
**Question:** What is the conclusion of the test? Test at a 10% significance level.
### Explanation:
This problem involves performing a hypothesis test for the difference in means using the t-distribution due to small sample sizes. The test statistic is calculated using the given sample means, standard deviations, and sizes. The p-value is then determined for the calculated test statistic, and the decision to reject or not reject the null hypothesis is made based on the p-value and the significance level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F915c192e-d8ba-4859-b60e-5e514228af12%2F85443582-7b4c-4ac3-8d8d-45c15d8a646a%2Fnk8xqur.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Using t-Distribution
**Problem Statement:**
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples and that the sample sizes are small. Also, assume the underlying distributions are relatively normal.
**Given Hypotheses:**
- Null Hypothesis (H₀): μ₁ = μ₂
- Alternative Hypothesis (H₁): μ₁ ≠ μ₂
**Sample Results:**
- Mean of sample 1 (x₁̄): 15.3
- Standard deviation of sample 1 (s₁): 11.6
- Sample size of sample 1 (n₁): 100
- Mean of sample 2 (x₂̄): 18.4
- Standard deviation of sample 2 (s₂): 14.3
- Sample size of sample 2 (n₂): 80
**(a) Calculate the Test Statistic and p-value:**
Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.
**Text Fields**:
- Test Statistic: [Input Field]
- p-value: [Input Field]
**(b) Conclusion of the Test:**
- **Radio Button Options:**
- Reject H₀
- Do not reject H₀
**Question:** What is the conclusion of the test? Test at a 10% significance level.
### Explanation:
This problem involves performing a hypothesis test for the difference in means using the t-distribution due to small sample sizes. The test statistic is calculated using the given sample means, standard deviations, and sizes. The p-value is then determined for the calculated test statistic, and the decision to reject or not reject the null hypothesis is made based on the p-value and the significance level.
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