Assume we have n = 20 i. i.d. observations x1, x2, xn from the exponential distribution with rate parameter λ. we want to test h0 : λ ≤ 8 vs. ha : λ > 8. develop a uniformly most powerful α = 0.05 level test and derive the rejection region of this test. (hint: when xi , 1 ≤ i ≤ n independently follows an exponential distribution of rate λ, then x : = pn i=1 xi ∼ gamma(n, λ), which has the density λ n γ(n) x n−1 e −λx, x > 0. use the quantile function shape = rate = lower. tail = in r to compute the cutoff value.)