If we are testing for the difference between the means of two independent populations with equal variances, samples of and are taken, then the number of degrees of freedom is equal to:
A) 29
B) 28
C) 14
D) 13
E) 11

Question

If we are testing for the difference between the means of two independent populations with equal variances, samples of  and  are taken, then the number of degrees of freedom is equal to:
A) 29 
B) 28 
C) 14 
D) 13 
E) 11

Quizplus · Accepted Answer

To calculate the number of degrees of freedom for a two-sample t-test, we use the formula: 
df = n1 + n2 - 2 
where n1 and n2 are the sample sizes of the two populations. 
Plugging in the given values, we get: 
df = 11 + 11 - 2 = 20 
However, since we are assuming equal variances, we use a pooled estimate of the variance, which reduces the degrees of freedom by one. 
Thus, the correct answer is: 
df = 11 + 11 - 2 -1 = 19 
which is closest to option B).

If We Are Testing for the Difference Between the Means