Question

in the t test for independent groups, the unbiased estimate of the population variance _______. select all that apply.
a. s1 2 alone
b. s2 2 alone
c. a weighted average of s1 2 and s2 2
d. (ss1 + ss2)/(n1 + n2 -2)

I know "d" is accurate but wondering if c is also. that is s1 squared and s2 squared, I believe.

Answer 1

The t statistic is given by:

$t = \frac{\bar X_1 - \bar X_2}{\sqrt{ \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}(\frac{1}{n_1}+\frac{1}{n_2}) } }$

The unbiased estimate of population variance for the t test for independent groups is given by:-

$\dpi{120} s^2 = { \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} }$

The answer is thus c. a weighted average of S²₁ and S²₂

D is wrong. It is not the arthimetic mean. (ss1 + ss2)/(n1 + n2 -2) is WRONG answer.