15 Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. Th ese needles need to have a...

2.3.15 Consider a manufacturing process that is producing

hypodermic needles that will be used for blood donations.

Th ese 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.

2.3.16 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?