For this problem, we are given the size of two populations, we are informed that their means are different, and we need to determine the degrees of freedom and critical values of t.
For this problem, we first need to determine the degrees of freedom, since we have two samples, we need to use the following formula:
Applying the size for both, we have:
Now we need to use the "t table" and look for the degree of freedom we found above:
The critical value is 1.684.