A certain population is strongly skewed to the right. We want to estimate its mean, so we will
Collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
A) II only
B) I only
C) II and III only
D) I and III only
E) III only

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample means will be approximately normal if the sample size is large enough, regardless of the population's distribution. Hence, statement II is true. Statement I is incorrect because the distribution of the sample data itself does not become normal with a larger sample size. Statement III is incorrect because the variability of the sample means decreases with a larger sample size.

A Certain Population Is Strongly Skewed to the Right