Question

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2)

A. (n1 + n2) degrees of freedom
B. (n1 + n2 - 1) degrees of freedom
C. (n1 + n2 - 2) degrees of freedom
D. n1 - n2 + 2

Answer 1

C. (n₁ + n₂ - 2) degrees of freedom

Explanation:

The t-test for difference between two mean when variance are equal is:

`t=\frac{\bar{x}_1-\bar{x}_2}{s\sqrt{(1)/(n_1)+(1)/(n_2)}}`

where ,

`\bar{x}_1` = Mean of Sample 1

`\bar{x}_2` = Mean of Sample 2

s = standard deviation

n_1 = size of Sample 1

n_2 = size of Sample 2

and t is Student's t-test with (n₁ + n₂ - 2) degrees of freedom.