Question

A quality control inspector must estimate the proportion of defective microcomputer chips coming from two different assembly operations. She knows that, among the chips in the lot to be inspected, 60% are from assembly operation A and 40% are from assembly operation B. Therefore, she takes a stratified random sample of 100 chips where 50 are randomly sampled from each operation. Among the sampled chips from operation A, six are defective. Among the sampled chips from operation B, ten are defective. Using this information, compute the estimated proportion of defective microcomputer chips for the lot. HINT: Look carefully at the formula for p̂(st). Is there a way to compute its value with only knowing the percentages as opposed to the population size of each stratum?

must use p̂(st)=(1/N)*(N₁p̂₁+N₂p̂₂+...+N_ip̂_i), where p̂_i=x_i/n_i)

Answer 1

Given that,

For operation A : N1 = 50, x1 = 6 and

For operation B : N2 = 50, x2 = 10 and

We want to find, the estimated proportion of defective microcomputer chips for the lot.

=> p̂(st) = 0.16