The Bankers report that in a sample of 120 consumer purchases in France, 60 were made with cash?

Question

The American Bankers Association reports that, in a sample of 120 consumer purchases in France, 60 were made with cash, compared with 26 in a sample of 50 consumer purchases in the United States. Construct a 90 percent confidence interval for the difference in proportions.

Answer 1

60/120 = 0.50

σ = √((0.5)(0.5)) = 0.50

σε ≈ 0.50/√120 ≈ 0.04564355

26/50 = 0.52

σ = √((0.52)(0.48))

σε ≈ √((0.52)(0.48)/(50) ≈ 0.07065409

∆μ = 0.02, or 2%

σε ≈ √(((0.50)(0.50) + (0.52)(0.48))/170) ≈ 0.05421092

P(- 0.0692 < ∆μ < 0.1092) = 90%