PROBLEM 3E

Let X have an exponential distribution with a mean of θ; that is, the pdf of X is f (x; θ) = (1/θ)e−x/θ , 0 < x < ∞. Let X1,X2, . . . ,Xn be a random sample from this distribution.

(a) Show that a best critical region for testing H0: θ = 3 against H1: θ = 5 can be based on the statistic

(c) If n = 12, find a best critical region of size α = 0.10 for testing H0: θ = 3 against H1: θ = 7.

(d) If H1: θ > 3, is the common region found in parts (b) and (c) a uniformly most powerful critical region of size α = 0.10?

Tuesday, February 21 st Chapter 7: Sampling Distributions 7.1 How Sample Proportions Vary Around the Population Proportion • Simulation: when we use a computer to pretend to draw random samples from some population of values over and...