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

Let X1, X2,..., Xn be a random sample from an exponential distribution with parameter λ. Then it can be shown that 2λ∑Xi has a chi-squared distribution with v = 2n (by first showing that 2λXi has a chi-squared distribution with v = 2).
a. Use this fact to obtain a test statistic for testing H0: μ = μ0. Then explain how you would determine the P-value when the alternative hypothesis is Ha: μ < μ0. [E(Xi) = μ = 1/λ, so μ = μ0 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
95 16 11 3 42 71 225 64 87 123
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.