i. If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed. ii. 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.
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) (ii) is a correct statement but not (i) and (iii).

Question

Quizplus · Accepted Answer

i. The statement about the null hypothesis is incorrect because testing for no difference between two means (e.g., between males and females) is typically a two-tailed test, not one-tailed. A one-tailed test would be used if the hypothesis specifically stated a direction (e.g., males earn more than females).ii. The statement about independence between samples is correct. When testing for differences between two population means, it's assumed that the samples are independent of each other unless specified otherwise (e.g., in paired samples).iii. The statement about degrees of freedom is incorrect. When testing for differences between two population means with small sample sizes (less than 30), the degrees of freedom for a t-test are based on the sample sizes of both groups, not simply n - 1. For two samples, it's more complicated and depends on both sample sizes and their variances.

I If the Null Hypothesis States That There Is No