(i. As the sample size (n) increases, the spread in the distribution of the sample means decreases. (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 correct because as sample size increases, the sample means will cluster more tightly around the true mean of the population, leading to a smaller spread in the distribution of the sample means.
(ii) is correct because if the entire population is sampled, there is no need for estimation and therefore no sampling error.
(iii) is correct under the central limit theorem, which states that as sample size increases, the sampling distribution of the mean approaches a normal distribution, even if the population itself is not normally distributed.

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