The sampling distribution of t differs from the sampling distribution of z in that _________.
A) there is only one sampling distribution of z (the normal distribution) for all N , while there are many sampling distributions for t , depending on sample size.
B) the sampling distribution of z is more narrow, except when N equals infinity.
C) the means of the two distributions are different
D) all of these
E) a and b

Question

Quizplus · Accepted Answer

Option A is correct because the sampling distribution of z follows the normal distribution, regardless of the sample size, while the sampling distribution of t follows the t-distribution, which changes depending on the sample size. 
Option B is also correct because the t-distribution has more variability than the normal distribution, resulting in wider tails (except when N equals infinity). 
Option C is incorrect because the means of both distributions are the same (zero) under the null hypothesis.

The Sampling Distribution of T Differs from the Sampling Distribution