Chapter 10.3, Problem 18P

Myers-Briggs: Marriage Counseling Most married couples have two or three personality preferences in common (see reference in Problem 17).

Myers used a random sample of 375 married couples and found that 132 had three preferences in common Another random sample of 571 couples showed that 217 had two personality preferences in common. Let $p_1$, be the population proportion of all married couples who have three personality preferences in common Let $p_2$ be the population proportion of all married couples who have two personality preferences in common.

(a) Find a 90% confidence interval for $p_1-p_2$.

(b) Interpretation Examine the confidence interval in part (a) and explain what it means in the context of this problem Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the proportion of married couples with three personality preferences in common compared with the proportion of couples withtwo preferences in common (at the 90% confidence level)?