Let X have a Bernoulli distribution with pmf We would like
Let X have a Bernoulli distribution with pmf
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
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.
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