Question

In: Statistics and Probability

The proportions of defective parts produced by two machines were compared, and the following data were...

The proportions of defective parts produced by two machines were compared, and the following data were collected. Determine a 95% confidence interval for p₁ - p₂. (Give your answers correct to three decimal places.)

Machine 1: n = 154; number of defective parts = 18

Machine 2: n = 142; number of defective parts = 6

Lower Limit
Upper Limit

Expert Solution

= 18/154 = 0.1169

= 6/142 = 0.0423

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

= (0.1169 * 154 + 0.0423 * 142)/(154 + 142)

= 0.0811

At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval for P1 - P2 is

() +/- z_0.025 * sqrt(P(1 - P)(1/n1 + 1/n2))

= (0.1169 - 0.0423) +/- 1.96 * sqrt(0.0811 * (1 - 0.0811) * (1/154 + 1/142))

= 0.0746 +/- 0.0623

= 0.0123, 0.1369

Lower limit = 0.0123

Upper limit = 0.1369

orchestra answered 2 years ago

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