When using the student's t distribution to test what value do you use for the degrees of freedom if the sample size is 32? O d.f.= 65 O d.f.=33 O d. f. = 31
When using the student's t distribution to test what value do you use for the degrees of freedom if the sample size is 32? O d.f.= 65 O d.f.=33 O d. f. = 31
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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![**Understanding Degrees of Freedom in Student's t-Distribution**
When using the student's t distribution to test the population mean ( \(\mu\) ), it is crucial to determine the appropriate degrees of freedom (d.f.). For any given t-distribution, the degrees of freedom are based on the sample size (n).
The general formula to calculate the degrees of freedom for a single sample in the t-distribution is:
\[ \text{Degrees of Freedom (d.f.)} = n - 1 \]
where \(n\) is the sample size.
**Example Problem:**
**Question:** When using the student's t distribution to test \( \mu \), what value do you use for the degrees of freedom if the sample size is 32?
**Answer Choices:**
- \( d.f. = 65 \)
- \( d.f. = 33 \)
- \( d.f. = 31 \)
- \( d.f. = 32 \)
- \( d.f. = 63 \)
**Solution:**
Given the sample size \( n = 32 \), the degrees of freedom are calculated as follows:
\[ \text{d.f.} = n - 1 = 32 - 1 = 31 \]
Therefore, the correct answer is:
- \( d.f. = 31 \)
**Conclusion:**
Understanding and applying the correct degrees of freedom is essential for accurate t-distribution analysis. In this example, with a sample size of 32, the t-distribution with 31 degrees of freedom is used.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6805edd-9acc-4ccd-9c7a-22df1558ea0b%2Fdaf72d8e-32f1-4047-b2d9-bd52027c4e16%2Fo12foj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Degrees of Freedom in Student's t-Distribution**
When using the student's t distribution to test the population mean ( \(\mu\) ), it is crucial to determine the appropriate degrees of freedom (d.f.). For any given t-distribution, the degrees of freedom are based on the sample size (n).
The general formula to calculate the degrees of freedom for a single sample in the t-distribution is:
\[ \text{Degrees of Freedom (d.f.)} = n - 1 \]
where \(n\) is the sample size.
**Example Problem:**
**Question:** When using the student's t distribution to test \( \mu \), what value do you use for the degrees of freedom if the sample size is 32?
**Answer Choices:**
- \( d.f. = 65 \)
- \( d.f. = 33 \)
- \( d.f. = 31 \)
- \( d.f. = 32 \)
- \( d.f. = 63 \)
**Solution:**
Given the sample size \( n = 32 \), the degrees of freedom are calculated as follows:
\[ \text{d.f.} = n - 1 = 32 - 1 = 31 \]
Therefore, the correct answer is:
- \( d.f. = 31 \)
**Conclusion:**
Understanding and applying the correct degrees of freedom is essential for accurate t-distribution analysis. In this example, with a sample size of 32, the t-distribution with 31 degrees of freedom is used.
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