Question

Most married couples have two or three personality preferences in common. A random sample of 371 married couples found that 130 had three preferences in common. Another random sample of 573 couples showed that 219 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 90% confidence interval for p1 – p2. (Round your answers to three decimal places.)

Lower limit:

Upper limit:

Answer 1

Pq Nora Answers - Given datar A random sample of married couples (n.) = 371 Another random sample of couples (N2) = 573. 71=130 and X2 = 219. Po - - 130 = 0.3504 Pe a Me 319 = 0.39213 Pi-Pe=0.3504-0.3821 = -0.0317. standard Error (se)pa-Pe Pict-P) PeC1-P) - 370 73 10.3504(1-0:3504) 0.3821 (1-0.3821) V 371 . . 573 0.2276 + 0.2360 11371 573 = 0.00061 +0.00041 =10.00102 =0.03192 we consider a 90% CI for Pi-Pa.. Za19 = 20.08 = 1.645 (from 2 table wing interpretation, ath A distance blw 1.64 and 1.65)

. Error = Z212 SEP-P2 =1:645 +0.0319 = 0.0524 (I is given by :(P1-P2) & Z12 SEP - P2 = -0.0317 + 0.0524 → (-0.0841,0.0207) lower limit : [0.0841 upper limit: 0.0207)