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 H0: p = .01 versus Ha: p > .01, where p is the actual 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 1% defective circuits.)
a. In this context, define Type I and Type II errors.
b. From the calculator manufacturer's point of view, which type of error is considered more serious?
c. From the printed circuit supplier's point of view, which type of error is considered more serious?
Water specimens are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150°F, there will be no negative effects on the river's ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 1508F, researchers will take 50 water specimens at randomly selected times and record the temperature of each specimen. The resulting data will be used to test the hypotheses H0: µ = 150°F versus Ha: µ . 150°F.
a. In the context of this example, describe Type I and Type II errors.
b. Which type of error would you consider more serious? Explain.