Problem

Suppose that a single observation X is taken from a uniform density on [0, θ], and consi...

Suppose that a single observation X is taken from a uniform density on [0, θ], and consider testing H0 : θ = 1 versus H1 : θ = 2.

a. Find a test that has significance level α = 0. What is its power?

b. For 0 < α < 1, consider the test that rejects when X ∈ [0, α]. What is its significance level and power?

c. What is the significance level and power of the test that rejects when X ∈ [1 − α, 1]?

d. Find another test that has the same significance level and power as the previous one.

e. Does the likelihood ratio test determine a unique rejection region?

f. What happens if the null and alternative hypotheses are interchanged—H0 : θ = 2 versus H1 : θ = 1?

Step-by-Step Solution

Request Professional Solution

Request Solution!

We need at least 10 more requests to produce the solution.

0 / 10 have requested this problem solution

The more requests, the faster the answer.

Request! (Login Required)


All students who have requested the solution will be notified once they are available.
Add your Solution
Textbook Solutions and Answers Search