A random sample of 362 married couples found that 286 had two or more personality preferences in common. In another random sample of 556 married couples, it was found that only 32 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common. A) Find a 95% confidence interval for p1 and p2.
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, a 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 95% 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.