Problem 11E

In a random sample of 100 parts ordered from vendor A, 12 were defective. In a random sample of 200 parts ordered from vendor B, 10 were defective.

a. Estimate the proportion of parts from vendor A that are defective, and find the uncertainty in the estimate.

b. Estimate the proportion of parts from vendor B that are defective, and find the uncertainty in the estimate.

c. Estimate the difference in the proportions, and find the uncertainty in the estimate.

Answer :

Step 1 of 4:

Given, we have two sample size, vender A ordered random sample of 100 parts, in that 12 were defectives.

vender B ordered random sample of 200 parts, in that 10 were defectives.

Let X follows binomial distribution with probability mass function is

P(x: n,p) = (1 - p , x = 0, 1, 2, ….., n.

Where,

n = sample size

= 5

x = random variable

p = probability of success

q = 1 - p (probability of failure)

The goal of the problem is

- We have to find the proportion of parts from part A that are defective and the uncertainty in the estimate.
- We have to find the proportion of parts from part B that are defective and the uncertainty in the estimat.
- We have to find the difference in the proportions, and the uncertainty in the estimate.