Find the rejection region - compute the power of the test

Question

Data is drawn from a binomial(5, θ) distribution, where θ is unknown.

Here is the table of probabilities p(x | θ) for 3 values of θ:x 0 1 2 3 4 5 θ = 0.5 0.031 0.156 0.313 0.313 0.156 0.031 θ = 0.6 0.010 0.077 0.230 0.346 0.259 0.078 θ = 0.8 0.000 0.006 0.051 0.205 0.410 0.328 You want to run a significance test on the value of θ. You have the following:

Null hypothesis: θ = 0.5.

Alternate hypotheses: θ > 0.5.

Significance level: α = .1.

(a) Find the rejection region.

(b) Compute the power of the test for each of the two hypotheses θ = 0.6 and θ = 0.8.

(c) Suppose you run an experiment and the data gives x = 4. Compute the p-value of this data.