Question

The distribution of the salaries of sustainability analysts is skewed to the right. If Shamma is interested in estimating the mean salary of a sample of sustainability analysts, which of the following is true?

The expected value of the sample mean will be less than the population mean for small sample sizes.


The sampling distribution of the mean will be right skewed provided that the sample size is sufficiently large.


The sampling distribution of the sample mean will also be approximately normal for sufficiently large sample sizes.


The sampling distribution will be left-skewed.

Answer 1

Explanation:

The correct answer is:

The expected value of the sample mean will be less than the population mean for small sample sizes.

This is due to the fact that the distribution of salaries for sustainability analysts is skewed to the right, which means that there are more low salaries and a few very high salaries. This can cause the mean to be pulled to the right, which can result in an overestimation of the population mean if the sample size is small.

As the sample size increases, the central limit theorem tells us that the sampling distribution of the mean will become approximately normal, regardless of the shape of the population distribution. This means that the sampling distribution of the mean will not be right-skewed or left-skewed, but rather symmetrical and bell-shaped. Therefore, the third and fourth options are incorrect.