Most married couples have two or three personality preferences in common. A rand

Question

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.)

Explanation / Answer

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]

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