Question

Consider two independent random samples with the following results

n₁=477 n₂=716

x₁=372 x₂=175

Use this data to find the 90% confidence interval for the true difference between the population proportions. show supporting work for each step that follows.

Find the point estimate that should be used in constructing the confidence interval. Round the answer 3 decimal points

Answer 1

1 = 372 / 477 = 0.780

2 = 175 / 716 = 0.244

Point estimate of difference between proportion = (1 - 2) = ( 0.780 - 0.244 ) = 0.536

90% confidence interval of p1 - p2 is

(1- 2) - Z * sqrt( 1 ( 1 - 1) / n1 + 2 ( 1 - 2) / n2) < p1 - p2 < (1- 2) + Z * sqrt( 1 ( 1 - 1) / n1 + 2 ( 1 - 2) / n2)

0.536 - 1.645 * sqrt( 0.78 * 0.22 / 477 + 0.244 * 0.756 / 716) < p1 - p2 <

0.536 + 1.645 * sqrt( 0.78 * 0.22 / 477 + 0.244 * 0.756 / 716)

0.495 < p1 - p2 < 0.577

90% CI is ( 0.475 , 0.577)