The test statistic
Follows a standard normal distribution if:
A) and the samples are dependent.
B) and the samples are dependent.
C) both and and the samples are dependent.
D) both and and the samples are independent.

Question

The test statistic ​  ​
Follows a standard normal distribution if:
A) and the samples are dependent. 
B) and the samples are dependent. 
C) both and and the samples are dependent. 
D) both and and the samples are independent.

Quizplus · Accepted Answer

The test statistic follows a standard normal distribution when both samples are independent and the sample sizes are sufficiently large (n1 ≥ 30 and n2 ≥ 30). The choices A, B, and C mention that the samples are dependent, which means that the assumption of independence is violated. Therefore, the best choice is D, which mentions that both samples are independent.

The Test Statistic ​ ​

The Test Statistic