Consider the series of examples in this section concerning service times in a queue. Suppose that the
Question:
a. Using Theorem 9.2.1, determine the test procedure that minimizes the sum of the probabilities of type I and type II errors.
b. Suppose that X1 = 4 and X2 = 3 are observed. Perform the test in part (a) to see whetherH0 is rejected.
c. Prove that the distribution of T, given thatH0 is true, is the gamma distribution with parameters 2 and 1/2.
d. Using Theorem 9.2.2, determine the test procedure with level at most 0.01 that has minimum probability of type II error. Hint: It looks like you need to solve a system of nonlinear equations, but for a level 0.01 test, the equations collapse to a single simple equation.
e. Suppose that X1 = 4 and X2 = 3 are observed. Perform the test in part (d) to see whetherH0 is rejected.
Distribution
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Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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