Share
Explore BrainMass

Type 1 error, Type II error, Consumers Risk and Producers Risk

A manufacturer of handheld calculators receives very 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 then used to test H0: pi = 0.05 versus HA: pi > 0.05, where is the true proportion of defectives in the shipment. If the null hypothesis is not rejected, the shipment is accepted, and the circuits are used in the production of the calculators. If the null hypothesis is rejected, the entire shipment is returned to the supplier due to inferior quality. (A shipment is defined to be of inferior quality if it contains more than 5% defectives.)

a) In this context, define type I and type II errors.
b) From the calculator manufacturer?s point of view, which type of error would be considered more serious and explain why?
c) From the printed circuit supplier?s point of view, which type of error would be considered more serious and explain why?

Solution Preview

a) In this context, define type I and type II errors.
Type I error, also known as an "error of the first kind", an ? error, or a "false positive": the error of rejecting a null hypothesis when it is actually true.

Type II error, also known as an "error of the second kind", a ? error, or a "false ...

Solution Summary

The solution gives definition and interpretations of type 1 error type II error, consumers risk and producers risk.

$2.19