Question

A random sample of 376 married couples found that 298 had two or more personality preferences in common. In another random sample of 562 married couples, it was found that only 26 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 99% confidence interval for p₁ – p₂. (Use 3 decimal places.)

lower limit
upper limit

Answer 1

p1cap = 298/376 = 0.7926
p2cap = 26/562 = 0.0463

pcap = (298 + 26)/(376 + 562) = 0.3454

SE = sqrt(0.3454*(1-0.3454)*(1/376 + 1/562))
SE = 0.0317

lower limit = (0.7926 - 0.0463 - 2.5758*0.0317) = 0.665

upper limit = (0.7926 - 0.0463 + 2.5758*0.0317) = 0.8280