i. If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population. ii. If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances.
iii. When sample sizes are less than 30, a test for the differences between two population means has n - 1 degrees of freedom.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

Statement (i) is true because the independence of samples is an assumption of the two-sample test for means. Statement (ii) is also true because two sample t-test assumes normality and equal variances. Statement (iii) is not entirely true since the degrees of freedom depend on the sample size of the two groups, but generally, when the sample size is less than 30, we use the t-distribution with n1 + n2 - 2 degrees of freedom.

I If We Are Testing for the Difference Between Two