Question

Two means are compared using t-test to assess the statistical significance of the difference between two samples. Size of the first sample is 17 and the size of the second sample is 13. How many degrees of freedom are associated with the critical t-value?

• A. 32
• B. 31
• C. 29
• D. 28

Hint:

Because we estimate two independent sample parameters ($\bar{X}_1$ and $\bar{X}_2$) to calculate the pooled variance, we lose exactly 2 degrees of freedom from the total combined sample size ($n_1 + n_2$).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
When comparing the means of two independent samples with an assumption of equal variances, we calculate a pooled two-sample student's $t$-statistic.
Key Formula or Approach:
The degrees of freedom ($df$) associated with a two-sample independent $t$-test is:
\[ df = n_1 + n_2 - 2 \]

Step 2: Detailed Explanation:
We are given:
Sample size of group 1, $n_1 = 17$
Sample size of group 2, $n_2 = 13$
Substitute these values into the degrees of freedom formula:
\[ df = 17 + 13 - 2 = 28 \]
Therefore, there are 28 degrees of freedom associated with the critical $t$-value.

Step 3: Final Answer
The correct option is (D).