Most married couples have two or three personality preferenc

Most married couples have two or three personality preferences in common. A random sample of 376 married couples found that 130 had three preferences in common. Another random sample of 564 couples showed that 214 had two personality preferences in common. Let p₁ be the population proportion of all married couples who have three personality preferences in common. Let p₂ be the population proportion of all married couples who have two personality preferences in common.

(a) Find a 99% confidence interval for p₁ – p₂. (Use 3 decimal places.)

lower limit

upper limit

Solution