Question

Suppose you want to test the notion that individuals perceive a greater height difference between men and women than actually exists, due to stereotyping. The true population difference between the height of men and women is an average of 5 inches.

You obtain a random sample of 400 individuals and record their perceptions of the mean difference in height between men and women. You find that the sample perceives the difference between men and women to average 6 inches. The sample standard deviation is 4 inches.

a) Calculate the standard error of the sample mean.

b) Using the plus/minus 2 standard errors rule of thumb, calculate the 95 percent confidence interval.

c) Can you infer from your sample that individuals perceive a greater difference than actually exists? Explain.

Answer 1

A.   Calculate the standard error of the sample mean.

The standard error of the sample mean = 4/sqrt(400) = 0.2

B.   Using the ±2 rule of thumb, calculate the 95 percent confidence interval.

6 - 2*0.2, 6 + 2*0.2

5.6, 6.4

C.  Can you infer from your sample that individuals perceive a greater difference than actually exists? Explain.

Yes, because the lower bound of the confidence interval 5.6 is greater than 5.