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Let’s suppose that a coin has probability of a Head either p=1/3 or p=2/3. I mus

ID: 3375182 • Letter: L

Question

Let’s suppose that a coin has probability of a Head either p=1/3 or p=2/3.
I must test.. H0 : p=1/3 Ha: p=2/3
I toss the coin 3 times and get X Heads. I decide to reject H0 in favor of Ha if X=2 or X=3. (Count of Heads X is the CSS for p.)
What are the two error probabilities alpha and beta for this test?
What is the power of this test at the alternative Ha? Let’s suppose that a coin has probability of a Head either p=1/3 or p=2/3.
I must test.. H0 : p=1/3 Ha: p=2/3
I toss the coin 3 times and get X Heads. I decide to reject H0 in favor of Ha if X=2 or X=3. (Count of Heads X is the CSS for p.)
What are the two error probabilities alpha and beta for this test?
What is the power of this test at the alternative Ha?
I must test.. H0 : p=1/3 Ha: p=2/3 I must test.. H0 : p=1/3 Ha: p=2/3
I toss the coin 3 times and get X Heads. I decide to reject H0 in favor of Ha if X=2 or X=3. (Count of Heads X is the CSS for p.)
What are the two error probabilities alpha and beta for this test?
What is the power of this test at the alternative Ha?

Explanation / Answer

alpha=P(reject H0, when H0 true)

alpha=P(X=2 or X=3, when p=1/3)

alpha=P(X=2)+P(X=3)= 0.2592593

beta=P(accept H0, when H1 true)

beta=P( X=1, p=2/3)

beta=P(X=1)= 0.2222222

power of test is 1-beta.

=1- 0.2222222=0.7777778

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