Answer:
b. Student-t with 48 degrees of freedom
Step-by-step explanation:
For this case we need to use a Two Sample t Test: equal variances.
Assumptions
When running 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".
Let and
be the sample means of two sets of data of size
and
respectively. We assume that the distribution's of x and y are:
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:
So on this case the best answer would be :
b. Student-t with 48 degrees of freedom