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) The standard error (0.5 inches) is an estimated value of the standard deviation of the sample mean.
B) If a new sample of n = 36 men's heights is collected, the standard error of the mean might not equal 0.5 inches.
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.

Question

Quizplus · Accepted Answer

The standard error of 0.5 inches indicates the standard deviation of the sample mean distribution, not the range within which 95% of sample means will fall. The 95% confidence interval would be wider, typically 1.96 times the standard error.

For a Randomly Selected Sample of N = 36 Men's