Question

A random sample of 374 married couples found that 288 had two or more personality preferences in common. In another random sample of 568 married couples, it was found that only 20 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 90% confidence interval for p1 – p2. (Use 3 decimal places.)

Answer 1

The variables X, n, and p' can be defined in the context of the problem. The normal distribution should be used for this problem.

Step-by-step explanation:

a.

X = 288, n = 374, p' = 288/374

b.

X represents the number of married couples in the sample who have two or more personality preferences in common, n represents the total number of married couples in the sample, and p' represents the sample proportion of married couples who have two or more personality preferences in common.

c.

The distribution that should be used for this problem is the normal distribution since the sample size is large (n > 30).