A manufacturer produces crankshafts for an automobile engine. The wear of the crankshaft after 100,000 miles (0.0001 inches) is of interest because it is likely to have an impact on warranty claims. A random sample of n = 15 shafts is tested and the mean equals = 2.78. It is known that = 0.9 and that wear is normally distributed.

(a) Test H₀ : = 3 versus H₁: 3 using = 0.05.

(b) What is the power of this test if = 3.25?