10. Being both quality and cost conscious, a major foreign manufacturer of compact disk players is contemplating their warranty policy. The standard warranty for compact disk players sold by competing producers is 1 year. The manufacturer is considering a 2 year warranty. The operating life until failure of your compact disk player has the density fðx; bÞ¼ðx= b2Þ expðx=bÞIð0;1Þ ðxÞ

for some value of b > 0, where x is measured in years.

(a) The manufacturer wants their exposure to warranty claims to be, on average, no more than 5 percent of the units sold. Find the values of b for which Pðx  2; bÞ¼ Ð 2 0 fðx;bÞdx  :05:

(b) Based on a random sample of size 50, design a uniformly most powerful level .10 test of the null hypothesis that b will be in the set of values you identified in (a).

(c) A nondestructive test of the disk players that determines their operating life until failure is applied to 50 players that are randomly chosen from the assembly line. The measurements resulted in x ¼ 4:27: Test the null hypothesis in (b).

(d) Plot the power curve of this test, and interpret its meaning to the management of the manufacturing firm.