Question: A manufacturer of hand-held calculators receives large shipments of printed circuit boards for the calculators from a supplier. It is too costly and time consuming to inspect all circuit boards in a shipment, so a sample from each shipment is inspected. Information form the sample is used to test the following hypotheses:

\[\begin{aligned} & Ho:\pi =.05 \\ & Ha:\pi >.05 \\ \end{aligned}\]

where \[\pi \] is the true proportion if defective circuit cards in the shipment. If the null hypothesis is not rejected, the shipment is accepted and the circuit cards are used in production of the calculators. If the null hypothesis is rejected, the entire shipment is returned to the supplier. (A shipment is defined to be inferior and not accepted if it contains more than 5% defective circuit boards.)

a. What are Type I and Type II errors?

b. What are the consequences (in the context of this problem) of a Type I and Type II error for the manufacturer?

c. From the manufacturer’s point of view, which type of error is considered more serious? Why?