Question

The proportions of defective parts produced by two machines were compared, and the following data were collected. Determine a 90% confidence interval for p₁ - p₂. (Give your answers correct to three decimal places.)

Machine 1: n = 148; number of defective parts = 13

Machine 2: n = 152; number of defective parts = 5

Lower Limit
Upper Limit

Answer 1

Ler , P1 be the population proportion for machine 1 and P2 be the population proportion for machine2

Now , the sample proportions are ,

p1=X1/n1=13/148=0.0878

p2=X2/n2=5/152=0.0329

The pooled estimate is ,

P=(X1+X2)/(n1+n2)=(13+5)/(148+152)=0.06

Q=1-P=0.94

Now , ; From standard normal distribution table

Therefore , the 90% confidence interval for p1-p2 is

Lower limit=0.010

Upper limit=0.100