Question

The American Bankers Association reported that, in a sample of 150 consumer purchases in France, 60 were made with cash, compared with 23 in a sample of 55 consumer purchases in the United States. Construct a 95 percent confidence interval for the difference in proportions. (Round your intermediate value and final answers to 4 decimal places.) The 95 percent confidence interval is from to .

Answer 1

Solution :

Given that,

n₁ = 150

x₁ = 60

₁ = x₁ / n₁ = 0.40

n₂ =55

x₂ = 23

₂ = x₂ / n₂ = 0.418

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.40 - 0.418

= -0.018

2)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error =   *

=  

=

= 0.152

3) Required interval is

Point estimate   Margin of error

-0.018   0.152

(-0.17, 0.134)

The 95 percent confidence interval is -0.17 to 0.134.