1. Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mm-too big and they would hurt the donor (even more than usual), too small and they would rupture the red blood cells, rendering the donated blood useless. Thus, the manufacturing process would have to be closely monitored to detect any significant departures from the desired diameter. During every shift, quality control personnel take a sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected.
a. Define the parameter of interest in the context of this study and assign an appropriate symbol to it.
b. State the appropriate null and alternative hypotheses using the symbol defined in (a).
c. Describe what a Type I error would be in this study. Also, describe the consequence of such an error in the context of this study.
d. Describe what a Type II error would be in this study. Also, describe the consequence of such an error in the context of this study.
2. Recall that the two errors discussed in this chapter were regarded as "false alarm" and "missed opportunity." In some fields, these errors are also regarded as "consumer's risk" and "producer's risk." With regard to the previous exercise about the hypodermic needle manufacturing process, do you think the Type I error is the consumer's risk or the producer's risk? What about the Type II error?