A manufacturer of hand-held calculators receives large shipments of printed circ

Question

A manufacturer of hand-held calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. Information from the sample is then used to test H_0: mu = 0.05 versus H_A: mu > 0.05 where mu is the true proportion of defective circuits in the shipment. If the null hypothesis is not rejected, the shipment is accepted, and the circuits are used in the production of calculators. If the null hypothesis is rejected, the entire shipment is returned to the supplier because of inferior quality (A shipment is defined to be of inferior quality if it contains more than 5% defective circuits.) a.) In this context, define Type I and Type Il Errors. b.) From the calculator manufacturer's point of view, which error is considered more serious and why? c.) From the circuit supplier's point of view, which type of error is considered more serious and why?

Explanation / Answer

a) Type I error is the false rejection of a true null Hypothesis. I.e in this case the proportion of defective circuits is equal to 0.05, so the shipment is acceptable, but the shipment is rejected.

The Type II error is the incorrect retention of a false null hypothesis. i.e in this case, the proportion of defective circuits is more than 0.05, so the shipment should be returned, but the shipment is accepted.

b) From the calculator manufacturers point of view, the Type II error is more serious as the shipment contains an unacceptable amount of defective circuits, but the shipment gets accepted, which could cause problems as he would then be manufacturing more faulty calculators which would give him a bad brand name and hence reduce sales in future.

c) From the circuit suppliers point of view, the Type I error is more serious as, although his consignment was acceptable, it gets rejected. This would incur losses in terms of logistics (transport to and fro) and having to recheck the circuits, check for problems and resending them.

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