Question

Most married couples have two or three personality preferences in common. A random sample of 375 married couples found that 134 had three preferences in common. Another random sample of 573 couples showed that 215 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

Solution :

Given that,

n₁ = 375

x₁ = 134

₁ = x₁ / n₁ = 0.357

n₂ =573

x₂ = 215

₂ = x₂ / n₂ = 0.375

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.357 - 0.375

= -0.018

2)

Our aim is to construct 90% confidence interval.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05 and 1- /2 = 0.950

= 1.645 (use z table)

Margin of error =   *

=

= 0.053

3) Required interval is

Point estimate   Margin of error

-0.018  0.053

(-0.018- 0.053, -0.018+  0.053)

(-0.07, 0.035)

lower limit = -0.07

upper limit = 0.035