Answer:
The random variable t is distributed , with the degrees of freedom
And the pooled variance can be founded with the following formula:
The degrees of freedom are given by:
So then the best answer for this case:
c. t-distributed with 43 degrees of freedom
Step-by-step explanation:
When we use a a two-sample equal-variance t-test, the basic assumptions are "that the distributions of the two populations are normal, and that the variances of the two distributions are the same".
Both are normally distributed but without the variance equal for both populations.
The system of hypothesis can be:
Null hypothesis:
Alternative hypothesis:
We can define the following random variable:
The random variable t is distributed , with the degrees of freedom
And the pooled variance can be founded with the following formula:
The degrees of freedom are given by:
c. t-distributed with 43 degrees of freedom