(i. As the sample size (n) increases, the spread in the distribution of the sample means increases. (ii) If the sampling size equals the population size, the sampling error is zero.
(iii) If a population is normally distributed, the sampling distribution of the mean is normally distributed.
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

(i) is false because as the sample size increases, the spread in the distribution of the sample means decreases, not increases, according to the Central Limit Theorem. (ii) is true because if the sample size equals the population size, then the sample is the population, and there is no sampling error. (iii) is true because according to the Central Limit Theorem, if a population is normally distributed, then the sampling distribution of the mean will also be normally distributed, regardless of the sample size.

(I as the Sample Size (N) Increases, the Spread in the Distribution