Question

You have a contract with an auto parts supplier to provide spark plugs, and you guarantee no more than 2% will be faulty. You believe your manufacturing process works and the error rate is actually 1% or even less.

Your customer just returned a shipment, saying that they selected 20 at random and found 2 faulty, an error rate of 10%.

Was the customer justified in returning the shipment (and not paying)? You ask your chief statistician the probability that the error rate is 10% and not 2%.

Answer 1

We will use a z-test for proportions to test the claim of the customer in this case:

Null Hypothesis, Ho: P_o <= 0.02

Alternate Hypothesis: Ha: P_o > 0.02

The formula for the same is:

Here, N = 20

p̂ = 0.10

Therefore, z = (0.10 - 0.02)/0.031

z = 2.58

From the z-table, we can see that the p-value< 0.05. Hence, we can reject the null hypothesis and say that the error rate is more than 2%. We can certainly say from the test that the error rate is more than 2% but cannot say that it is 10%. Hence, the customer is right.