Question

The American Bankers Association reported that, in a sample of 100 consumer purchases in France, 49 were made with cash, compared with 31 in a sample of 60 consumer purchases in the United States.

Construct a 99 percent confidence interval for the difference in proportions. (Round your intermediate value and final answers to 4 decimal places.)

The 99 percent confidence interval is from ____ to ____.

Answer 1

Solution:

Given:

France:

Sample size = n₁ = 100

x₁ = 49

United States:

Sample size = n₂ = 60

x₂ = 31

We have to construct a 99 percent confidence interval for the difference in proportions

where

Z_c is z critical value for c = 0.99 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.99 ) / 2 = 1.99 /2 = 0.9950

Thus look in z table for Area = 0.9950 or its closest area and find corresponding z critical value.

From above table we can see area 0.9950 is in between 0.9949 and 0.9951 and both are at same distance from 0.9950, Hence corresponding z values are 2.57 and 2.58

Thus average of both z values is 2.575

Thus Z_c = 2.575

Thus

Thus

Thus :

The 99 percent confidence interval is from -0.2369 to 0.1835