Chapter 10.3, Problem 17P

Myers-Briggs: Marriage Counseling Isabel Myers was a pioneer in the study of personality types. She identified four basic personality preferences that are described at length in the book Manual: A Guide to the Development and Vie of the Myers-Briggs Type Indicator, by Myers and McCaulley (Consulting Psychologists Press). Marriage counselors know that couples who have none of the four preferences in common may have a stormy marriage. Myers took a random sample of 375 married couples and found that $2\times 9$ had two or more personality preferences in common. In another random sample of 571 married couples, it was found that only 23 had no preferences in common. Let $p_1$ be the population proportion of all married couples who have two or more personality preferences in common. Let $p_2$ be the population proportion of all married couples who have no personality preferences in common (a) Find a 99% confidence interval for $p_1-p_2.$

(h) Interpretation Explain the meaning of the confidence interval in part (a) 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 (at the 99% confidence level) about the proportion of married couples with two or more personality preferences in common compared with the proportion of married couples sharing no personality preferences in common ?