The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with kg.

Let m denote the true average weight reading on the scale.

a. What hypotheses should be tested?

b. Suppose the scale is to be recalibrated if either or . What is the probability that recalibration is carried out when it is actually unnecessary?

c. What is the probability that recalibration is judged unnecessary when in fact ? When ?

d. Let . For what value c is the rejection region of part

(b) equivalent to the “two-tailed”

region of either or ?

e. If the sample size were only 10 rather than 25, how should the procedure of part

(d) be altered so that ?

f. Using the test of part (e), what would you conclude from the following sample data?

9.981 10.006 9.857 10.107 9.888 9.728 10.439 10.214 10.190 9.793 g. Reexpress the test procedure of part

(b) in terms of the standardized test statistic .