A researcher conducts a hypothesis test uUsing a sample of n= 20 with M 34 and s = 36 from an unknown population. What is the df value for the t statistic? O df = 19 O df = 35 O df = 21 df = 37

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**Hypothesis Testing and Degrees of Freedom**

In this educational example, a researcher conducts a hypothesis test using a sample size of \( n = 20 \) with a sample mean \( M = 34 \) and a sample variance \( s^2 = 36 \) from an unknown population. The question posed is: What is the degrees of freedom (\( df \)) value for the \( t \) statistic?

The options provided are:
- \( df = 19 \)
- \( df = 35 \)
- \( df = 21 \)
- \( df = 37 \)

**Explanation:**

In statistical testing, the degrees of freedom for a single-sample t-test is calculated using the formula:

\[
df = n - 1
\]

Given that the sample size \( n = 20 \), we can determine the degrees of freedom as follows:

\[
df = 20 - 1 = 19
\]

Therefore, the correct answer is \( df = 19 \). This value is crucial for determining the critical value from the \( t \)-distribution table to assess statistical significance.
Transcribed Image Text:**Hypothesis Testing and Degrees of Freedom** In this educational example, a researcher conducts a hypothesis test using a sample size of \( n = 20 \) with a sample mean \( M = 34 \) and a sample variance \( s^2 = 36 \) from an unknown population. The question posed is: What is the degrees of freedom (\( df \)) value for the \( t \) statistic? The options provided are: - \( df = 19 \) - \( df = 35 \) - \( df = 21 \) - \( df = 37 \) **Explanation:** In statistical testing, the degrees of freedom for a single-sample t-test is calculated using the formula: \[ df = n - 1 \] Given that the sample size \( n = 20 \), we can determine the degrees of freedom as follows: \[ df = 20 - 1 = 19 \] Therefore, the correct answer is \( df = 19 \). This value is crucial for determining the critical value from the \( t \)-distribution table to assess statistical significance.
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