PROBLEM 7E

Let X1,X2, . . . ,X10 be a random sample of size 10 from a Poisson distribution with mean μ.

(a) Show that a uniformly most powerful critical region for testing H0: μ = 0.5 against H1: μ > 0.5 can be defined with the use of the statistic

(b) What is a uniformly most powerful critical region of size α = 0.068? Recall that has a Poisson distribution with mean 10μ.

(c) Sketch the power function of this test.

Psych Stats Powerpoint 6 ● we can identify important sections of the normal distribution using z- scores ● because we know what percent of scores falls in each part of the distribution, we can define the normal distribution in terms of proportions ○ these percentages/proportions apply to any normal distribution, regardless of the values for the mean and SD ● 68-95-99.7% rule ● if you know the z-score, you can find the proportion above or below that score using the unit normal table Unit Normal Table ● lists proportions of the normal distribution for a range of possible z- score values ● imagine you draw a line at a particular z-score ○ t