94. A service station has six gas pumps. When no vehicles are at the station, let pi denote the probability that the next vehicle will select pump i (i1, 2, . . . , 6). Based on a sample of size n, we wish to test H0:

p1  . . .  p6 versus Ha: p1  p3  p5, p2  p4  p6

(note that Ha is not a simple hypothesis). Let X be the number of customers in the sample that select an even-numbered pump.

a. Show that the likelihood ratio test rejects H0 if either X  c or X n 

c. (Hint: When Ha is true, let u denote the common value of p2, p4, and p6.)

b. Let n  10 and c  9. Determine the power of the test both when H0 is true and also when p2  p4  p6  . 1 10, p1  p3  p5  7 30