# Question: Let X1 X2 Xn be a

Let X1, X2, . . . , Xn be a random sample from the normal distribution N(μ, 9). To test the hypothesis H0: μ = 80 against H1: μ ≠ 80, consider the following three critical regions: C1 = {: ≥ C1}, C2 = {: ≤ C2}, and C3 = {: | − 80| ≥ C3}.

(a) If n = 16, find the values of C1, C2, C3 such that the size of each critical region is 0.05. That is, find C1, C2, C3 such that

(b) On the same graph paper, sketch the power functions for these three critical regions.

(a) If n = 16, find the values of C1, C2, C3 such that the size of each critical region is 0.05. That is, find C1, C2, C3 such that

(b) On the same graph paper, sketch the power functions for these three critical regions.

**View Solution:**## Answer to relevant Questions

Consider a random sample X1, X2, . . . , Xn from a distribution with pdf f(x; θ) = θ(1 − x)θ−1, 0 < x < 1, where 0 < θ. Find the form of the uniformly most powerful test of H0: θ = 1 against H1: θ > 1. Let X1, X2, ... , Xn be a random sample from an exponential distribution with mean θ. Show that the likelihood ratio test of H0: θ = θ0 against H1: θ ≠ θ0 has a critical region of the form How would you modify this ...In a psychology experiment, 140 students were divided into majors emphasizing left-hemisphere brain skills (e.g., philosophy, physics, and mathematics) and majors emphasizing right-hemisphere skills (e.g., art, music, ...Let μi be the average yield in bushels per acre of variety i of corn, i = 1, 2, 3, 4. In order to test the hypothesis H0: μ1 = μ2 = μ3 = μ4 at the 5% significance level, four test plots for each of the four varieties of ...In a college health fitness program, let X equal the weight in kilograms of a female freshman at the beginning of the program and let Y equal her change in weight during the semester. We shall use the following data for n = ...Post your question