Let X1, X2, …., Xn be a random sample from an exponential distribution with parameter l...

Let X₁, X₂, …., X_n be a random sample from an exponential distribution with parameter l. Then it can be shown that λ Then it can be shown that has a chi-squared distribution with v = 2n (by first showing that has a chi-squared distribution with v = 2).

a. Use this fact to obtain a test statistic and rejection region that together specify a level a test for H₀: μ = μ₀ versus each of the three commonly encountered alternatives is equivalent to λ = 1/μ₀ ].

b. Suppose that ten identical components, each having exponentially distributed time until failure, are tested. The resulting failure times are

Use the test procedure of part (a) to decide whether the data strongly suggests that the true average lifetime is less than the previously claimed value of 75.