Most married couples have two or three personality preferences in common. A random sample of371married couples found that134had three preferences in common. Another random sample of569couples showed that215had two personality preferences in common. Letp₁be the population proportion of all married couples who have three personality preferences in common. Letp₂be the population proportion of all married couples who have two personality preferences in common.

(a) Find a 90% confidence interval forp₁-p₂. (Round your answers to three decimal places.)

• lower limit=
• upper limit=

(b) 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 with two preferences in common (at the 90% confidence level)?

• 1. Because the interval contains only positive numbers, we can say that a higher proportion of married couples have three personality preferences in common.
• 2. Because the interval contains both positive and negative numbers, we can not say that a higher proportion of married couples have three personality preferences in common.
• 3. We can not make any conclusions using this confidence interval.
• 4. Because the interval contains only negative numbers, we can say that a higher proportion of married couples have two personality preferences in common.