Question

For a randomly selected sample of n = 36 men’s heights, it is reported that the standard error of the mean is 0.5 inches. Three of the following statements are true, while one is false. Which statement is false?

A. If a new sample of n = 36 men’s heights is collected, the standard error of the mean might not equal 0.5 inches.

B. The standard error (0.5 inches) is an estimated value of the standard deviation of the sample mean.

C. Over many different samples of n = 36 men’s heights, the average difference between the sample mean and population mean will be roughly 0.5 inches.

D. In about 95% of all samples of n = 36 men’s heights, the sample mean will be within 0.5 inches of the population mean.

Answer 1

Option(D) is the answer.

Reason:

If a new sample of n = 36 men’s heights is collected, the standard error of the mean might not equal 0.5 inches.(True)

The standard error (0.5 inches) is an estimated value of the standard deviation of the sample mean.(True)

Over many different samples of n = 36 men’s heights, the average difference between the sample mean and population mean will be roughly 0.5 inches.(True)

In about 95% of all samples of n = 36 men’s heights, the sample mean will be within 0.5 inches of the population mean.(False)

Therefore, Option(D) is the answer.

thank you.