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

Question

Quizplus · Accepted Answer

II only. According to the Central Limit Theorem, as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the shape of the population distribution. This does not necessarily mean the distribution of the sample data itself will be closer to normal (I is incorrect), nor does it imply that the variability of the sample means will be greater; in fact, larger samples typically lead to less variability in the sample means (III is incorrect).

A Certain Population Is Strongly Skewed to the Right