Let be a random sample from an exponentialdistribution with parameter l. Then it can be
Chapter 8, Problem 85(choose chapter or problem)
Let be a random sample from an exponentialdistribution with parameter l. Then it can be shown thathas a chi-squared distribution with (by firstshowing that has a chi-squared distribution with ).a. Use this fact to obtain a test statistic and rejection regionthat together specify a level a test for versuseach of the three commonly encountered alternatives.[Hint: , so is equivalent to.]b. Suppose that ten identical components, each havingexponentially distributed time until failure, are tested.The resulting failure times are95 16 11 3 42 71 225 64 87 123Use the test procedure of part (a) to decide whether the datastrongly suggests that the true average lifetime is less thanthe previously claimed value of 75.
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