Question

The proportions of defective parts produced by two machines were compared, and the following data were collected. Determine a 98% confidence interval for p₁ - p₂. (Give your answers correct to three decimal places.)

Machine 1: n = 153; number of defective parts = 9

Machine 2: n = 155; number of defective parts = 9

Lower Limit -

Upper Limit -

Answer 1

= 9/153 = 0.0588, 1 - = 0.9412, n₁ = 153,

= 9/155 = 0.0581 1 - = 0.9419, n₂ = 155,

The Zcritical (2 tail) for = 0.02, is 2.326

The Confidence Interval is given by (- ) ME, where

(- ) = 0.0588 – 0.0581 = 0.0007

The Lower Limit = 0.0007 - 0.0622 = - 0.0615    -0.062

The Upper Limit = 0.0007 + 0.0622 = 0.0629    0.063