In: Statistics and Probability
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%.
We are to test here whether the error rate is < 2% that is 0.02. The sample proportion here is given as: p = 0.1 with sample size n = 20
The test statistic thus is computed here as:
Now the probability that the error rate is 10% given that the true error rate is 2% is computed here as:
Getting it from the standard normal tables, we get here:
Therefore the p-value here is very low here < 0.01, and therefore there is a very low probability that the error rate is less than 2%.
Therefore the customer is justified in returning the shipment ( and not paying )