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The American Bankers Association reported that, in a sample of 125 consumer purchases in France, 63...

The American Bankers Association reported that, in a sample of 125 consumer purchases in France, 63 were made with cash, compared with 26 in a sample of 50 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 _______ .

Solutions

Expert Solution

Solution :

Given that,

= x1 / n1 = 63 / 125 = 0.504

1- = 0.496

= x2 / n2 = 26 / 50 = 0.52

1 - = 0.48

At 95% confidence level the z is ,

Z/2 = 1.96

95% confidence interval for p1 - p2 is ,

( - )   Z/2  * [(1- ) / n1 + (1 - ) / n2]

(0.504 - 0.52)   1.96 * [(0.504 * 0.496) / 125 + (0.52 * 0.48 ) / 50]

-0.180 < p1 - p2 < 0.148

(-0.180 , 0.148)

-0.180 to 0.148

milcah answered 9 months ago
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