1.) A manufacturer of hand-held calculators receives large shipments of printed

Question

1.) 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 HO: µ = 0.05 versus HA: µ > 0.05 where µ 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 II 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) In statistical hypothesis testing, a type I erroris the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is incorrectly retaining a false null hypothesis (a "false negative").

Now in given context Type I error is entire shipment is returned to the supplier all though the shipment was not of inferior quality

And Type II error is retaining the shipment all though the shipment was of inferior quality.

b) From manufacturer’s point of view, type II error is more dangerous as it will lead to defective calculators and as a result company will be in losses.

c) From circuit supplier’s point of view, Type I error is dangerous because all though their shipment was not inferior still it was rejected. Which will give loss to them as they have to recollect the shipment and recheck it.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.