Suppose the (sample) average height of women in the U.S . is = 161.8cm, and the average height of men in the U.S . is = 175.4cm. For both the sample standard deviation is about s = 7.62cm.

(a) Suppose you take a sample of 7 women and 7 men. Construct a 95% CI for both. Do the confidence intervals overlap?

(b) Now repeat using a sample of 175 women and 200 men. Do the confidence intervals overlap?

(c) Can you explain what happened? Why is sample size important if you're trying to find differences between groups?