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 20 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

Given that, n1 = n2 = 300, x1= 20 and x2 = 8

Using TI-84 calculator we get, 99% confidence interval for the difference in two fractions (p1 - p2) is, ( -0.004, 0.084 )

Where, lower bound = -0.004 and upper bound = 0.084

Therefore,  a 99% lower bound on the difference in the two fractions (p1-p2) is -0.004