Question

To conduct a two-sample test of hypothesis with independent samples, what must be true? a) The sample size from each population must be the same. b) The members in both populations must be related. c) The populations must come from different geographic areas. d) Both samples must measure the same parameter (wages, age, preference, etc.) from their respective populations.

Answer 1

Solution:

Given question is: To conduct a two-sample test of hypothesis with independent samples, what must be true?

For two-sample test of hypothesis with independent samples, we must have two independent population and corresponding samples, that is two samples should not be dependent or members of one group should not be related to members of other group. Also samples are independent , so sample size in both sample can be different.

Thus option a and b are incorrect or false regarding  two-sample test of hypothesis with independent samples.

For  two-sample test of hypothesis with independent samples, we can collect two independent samples from same geographic areas, so option c) is also not true.

For  two-sample test of hypothesis with independent samples, we must measure same kind of parameter and same kind variable in both samples.

For example: In case of comparing mean marks of Male students and Female students, we have two independent samples of Male and Female. But we are using same parameter Mean marks of both samples.

Thus correct option or true statement regarding, "To conduct a two-sample test of hypothesis with independent samples", is:

d) Both samples must measure the same parameter (wages, age, preference, etc.) from their respective populations.