Question

If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to a. 38. b. 19. c. 18. d. 39.

Answer 1

Answer:

Null hypothesis: $\mu_1= \mu_2$

Alternative hypothesis:$\mu_1 =\neq \mu_2$

And for this case we assume that we have equal variances so that means:

$\sigma =\sigma_1 =\sigma_2$

For this case the degrees of freedom are given by:

$df= n_1 +n_2 -2$

And replacing we got:

$df= 20+20 -2= 38$

And the best answer would be:

a. 38

Step-by-step explanation:

For this problem we want to test the following:

Null hypothesis: $\mu_1= \mu_2$

Alternative hypothesis:$\mu_1 =\neq \mu_2$

And for this case we assume that we have equal variances so that means:

$\sigma =\sigma_1 =\sigma_2$

For this case the degrees of freedom are given by:

$df= n_1 +n_2 -2$

And replacing we got:

$df= 20+20 -2= 38$

And the best answer would be:

a. 38