Because of variability in the manufacturing process, the actual yielding point of a sample of mild steel subjected to increasing stress will usually differ from the theoretical yielding point. Let p denote the true proportion of samples that yield before their theoretical yielding point. If on the basis of a sample it can be concluded that more than 20% of all specimens yield before the theoretical point, the production process will have to be modified.

a. If 15 of 60 specimens yield before the theoretical point, what is the P-value when the appropriate test is used, and what would you advise the company to do?

a 5 .01 n 5 855 H n 5 176 a: m 2 5.63 H0 P-value . .10 : m 5 5.63 n 5 24, t 5 2.2 n 5 9, t 5 1.8, a 5 .01 n 5 15, t 5 3.2, a 5 .05

b. If the true percentage of “early yields” is actually 50%

(so that the theoretical point is the median of the yield distribution) and a level .01 test is used, what is the probability that the company concludes a modification of the process is necessary?