Question

Consider two independent random samples with the following results: n 1 =160 x 1 =84     n 2 =95 x 2 =72 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 = 84 / 160 = 0.525

1- = 0.475

= x₂ / n₂ = 72 / 95 = 0.758

1 - = 0.242

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]

(0.525 - 0.758)   1.645* [(0.525 * 0.475) / 160 + (0.758 * 0.242) / 95]  

-0.330 < p₁ - p₂ < -0.136

(-0.330 , -0.136)