Question

Two different types of injection-moulding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 300, are selected, and 12 defective parts are found in the sample from machine 1, and 8 defective parts are found in the sample from machine 2. Construct a 99% lower bound on the difference in the two fractions (p₁-p₂). Please report your answer to 3 decimals.

Answer 1

solution:

Given data

x1 = 12

n1 = 300

x2 = 8

n2 = 300

  1 = x1/n1 = 12/300 = 0.04

    2 = x2/n2 = 8/300 = 0.0267

For 99% confidence level , = 1 - CL = 1 - 0.99 = 0.01

critical value: Z(/2) = Z(0.005) = 2.576 [use z distribution table ]

The confidence interval for difference of two proportions is given by

CI : ( 1-2) ± Z *

:(0.04 - 0.0267) ± 2.576 *

: 0.0133   ± 0.0377

: (-0.0244 , 0.051)

:( -0.024 , 0.051)

Therefore , 99% confidence interval for difference of two proportions is -0.024 < p1-p2 < 0.051