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.)

Solution

CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
Probability Succuses( X1 )=130
No.Of Observed (n1)=376
P1= X1/n1=0.346
Proportion 2
Probability Succuses(X2)=214
No.Of Observed (n2)=564
P2= X2/n2=0.379
C.I = (0.346-0.379) ±Z a/2 * Sqrt( (0.346*0.654/376) + (0.379*0.621/564) )
=(0.346-0.379) ± 2.58* Sqrt(0.001)
=-0.034-0.082,-0.034+0.082
=[-0.116,0.049]