PROBLEM 8E

Let X have a Bernoulli distribution with pmf

f (x; p) = px(1 − p)1−x, x = 0, 1, 0 ≤ p ≤ 1.

We would like to test the null hypothesis H0: p ≤ 0.4 against the alternative hypothesis H1: p > 0.4. For the test statistic, use where X1,X2, . . . ,Xn is a random sample of size n from this Bernoulli distribution. Let the critical region be of the form C = {y: y ≥ c}.

(a) Let n = 100. On the same set of axes, sketch the graphs of the power functions corresponding to the three critical regions, C1 = {y : y ≥ 40}, C2 = {y :y ≥ 50}, and C3 = {y : y ≥ 60}. Use the normal approximation to compute the probabilities.

(b) Let C = {y : y ≥ 0.45n}. On the same set of axes, sketch the graphs of the power functions corresponding to the three samples of sizes 10, 100, and 1000.

MKT 210 – Principles of Marketing Dr. Thomas Burnham Fall 2016 BizCafe – Assignment #5 Instructions Game Schedule Game Open: Tuesday, 11/08 at 8:00 a.m. Game Close: Tuesday, 11/15 at 4:00 p.m. Course Points A maximum of 10 points will be available for performance in this game. Five points will be given for completing the game (all 16 periods) on time. One to five points will be given based on your cumulative retained earnings RELATIVE to the rest of the class AND FOLLOWING THE RULES. The maximum you will receive if you do not follow the rules is five points! Background & Notes You may collaborate with your classmates in working on Bizcafe – that is, you may discuss with others in the