The number of degrees of freedom for the t-test for the difference between the means of two independent populations with unequal variances and sample sizes n1 and n2 can be calculated using the following formula:
df = [(s1^2/n1 + s2^2/n2)^2] / [((s1^2/n1)^2)/(n1 - 1) + ((s2^2/n2)^2)/(n2 - 1)]
where s1 and s2 are the sample standard deviations of the two populations.
Substituting the given values, we get:
df = [(s1^2/20 + s2^2/20)^2] / [((s1^2/20)^2)/19 + ((s2^2/20)^2)/19]
Since the values of s1 and s2 are not given, we cannot compute the value of df. However, in general, the degrees of freedom for a t-test with sample sizes of 20 and equal variances would be 38 (assuming a two-tailed test and a significance level of 0.05).