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 only
B) II and III only
C) I and III only
D) III only
E) I only

Question

Quizplus · Accepted Answer

A large sample will more accurately reflect the skewness of the population, so the distribution of the sample data will be more clearly skewed to the left. However, the Central Limit Theorem states that the sampling distribution of the sample means will be approximately normal, not skewed, and the variability of the sample means will decrease with larger samples.

A Certain Population Is Strongly Skewed to the Left