A certain population is strongly skewed to the left. We want to estimate its mean, so we 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 more clearly skewed to the left.
II. The sampling model of the sample means will be more skewed to the left.
III. The variability of the sample means will greater.
A) II and III only
B) III only
C) II only
D) I and III only
E) I only

Question

Quizplus · Accepted Answer

A larger sample size will make the distribution of the sample data more clearly reflect the skewness of the population. However, the sampling distribution of the sample means will become more normal (less skewed) due to the Central Limit Theorem, and the variability of the sample means will decrease with a larger sample size.

A Certain Population Is Strongly Skewed to the Left