An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value if n = 5 and T = -0.96. Assume you are doing a two-tailed test. p-value: What decision do we make with the null hypothesis at a = 0.05? p-value: O Reject H O Fail to reject H
An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value if n = 5 and T = -0.96. Assume you are doing a two-tailed test. p-value: What decision do we make with the null hypothesis at a = 0.05? p-value: O Reject H O Fail to reject H
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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how do i find the p-value?
![### Hypothesis Testing Example
**Problem Statement:**
An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value if \( n = 5 \) and \( T = -0.96 \). Assume you are doing a two-tailed test.
**Step 1: Determine the p-value**
p-value: [__________]
**Step 2: Decision Making Based on the Null Hypothesis**
What decision do we make with the null hypothesis at \( \alpha = 0.05 \)?
**Choices:**
- [ ] Reject \( H_0 \)
- [ ] Fail to reject \( H_0 \)
**Explanation of Terms:**
- **n:** The sample size, which is 5.
- **T:** The test statistic, which is -0.96.
- **p-value:** A measure of the evidence against the null hypothesis. The smaller the p-value, the stronger the evidence to reject the null hypothesis.
- **\(\alpha = 0.05\):** The significance level, which represents the probability of rejecting the null hypothesis when it is actually true.
**Decision Rule:**
- If the p-value is less than \(\alpha\), we reject the null hypothesis (\( H_0 \)).
- If the p-value is greater than or equal to \(\alpha\), we fail to reject the null hypothesis (\( H_0 \)).
This exercise helps in understanding how to conduct a hypothesis test for a sample from an approximately normal population with an unknown standard deviation, using a t-distribution.
**Note:** There are no graphs or diagrams provided in this image that need detailed explanation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8e28faf-547f-4c48-bb6d-e40546588d1c%2F455a3d77-8514-4e25-a26d-13edfe0d2215%2Fti2rss_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Example
**Problem Statement:**
An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value if \( n = 5 \) and \( T = -0.96 \). Assume you are doing a two-tailed test.
**Step 1: Determine the p-value**
p-value: [__________]
**Step 2: Decision Making Based on the Null Hypothesis**
What decision do we make with the null hypothesis at \( \alpha = 0.05 \)?
**Choices:**
- [ ] Reject \( H_0 \)
- [ ] Fail to reject \( H_0 \)
**Explanation of Terms:**
- **n:** The sample size, which is 5.
- **T:** The test statistic, which is -0.96.
- **p-value:** A measure of the evidence against the null hypothesis. The smaller the p-value, the stronger the evidence to reject the null hypothesis.
- **\(\alpha = 0.05\):** The significance level, which represents the probability of rejecting the null hypothesis when it is actually true.
**Decision Rule:**
- If the p-value is less than \(\alpha\), we reject the null hypothesis (\( H_0 \)).
- If the p-value is greater than or equal to \(\alpha\), we fail to reject the null hypothesis (\( H_0 \)).
This exercise helps in understanding how to conduct a hypothesis test for a sample from an approximately normal population with an unknown standard deviation, using a t-distribution.
**Note:** There are no graphs or diagrams provided in this image that need detailed explanation.
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