Question

Two different types of injection-molding 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 it was found that p1 -0.05 and p2 -0.01. Is it reasonable to conclude that both machines produce the same fraction of defective parts, using alpha = 0.057 Determine the sample size needed to detect this difference with a probability of at least 0.9 Use at least 2 decimal digits

Answer 1

Answer:

Given,

p1 = 0.05 , p2 = 0.01

alpha = 0.05

Here at 95% confidence level, z value is 1.96

sample size n = (z(alpha)*sqrt((p1+p2)(q1+q2)/2) + z(beta)*sqrt(p1q1+p2q2))^2 / (p1-p2)^2

substitute values

= (1.96*sqrt(0.05+0.01)(0.95+0.99)/2) + 1.28*sqrt(0.05*0.95+0.01*0.99))^2 / (0.05-0.01)^2

= 379.77

sample n = 380