Question

Consider two independent random samples with the following results: n1 =653 x1 =355     n2 =597 x2 =201 Use this data to find the 90% confidence interval for the true difference between the population proportions. Copy Data Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

= x₁ / n₁ = 355 / 653 = 0.544

1- = 0.456

= x₂ / n₂ = 201 / 597 = 0.337

1 - = 0.663

At 90% confidence level the z is ,

Z_/2 = Z _0.05 = 1.645

90% confidence interval for p₁ - p₂ is ,

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

(0.544 - 0.337)   1.645 * [(0.544 * 0.456) / 653 + (0.337 * 0.663) / 597]

0.162 < p₁ - p₂ < 0.252

(0.162 , 0.252)