Probability question -- A test to see if a coin is fair....

[Mr Davis 97]

Homework Statement

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You want to see if a coin is fair. You flip it 5 times and count the number of heads. If H is the number of heads obtained in five flips of the coin, what is the P-value of the test when H equals 4?

Homework Equations

None

The Attempt at a Solution

To solve this problem, I thought that it would be correct to use the binomial PDF, to answer the question "If the probability of getting heads is .5, then what are the chances of getting 4 heads in 5 flips?" This gives .15625, which is not the right P-value. The correct answer is 3/16, but how do I get this value? What probability distribution to I use to obtain this P-value?

 

[Orodruin]

The p-value is not the probability of landing on the exact outcome. It is the probability of obtaining that or a more extreme outcome. I would also disagree on how the "correct" answer has chosen to define an outcome as extreme (getting 1 head is as extreme as getting 4, getting 0 is as extreme as getting 5 - you would typically not design a test which broke the symmetry).

 

[Ray Vickson]

Homework Statement

[/B]
You want to see if a coin is fair. You flip it 5 times and count the number of heads. If H is the number of heads obtained in five flips of the coin, what is the P-value of the test when H equals 4?

Homework Equations

None

The Attempt at a Solution

To solve this problem, I thought that it would be correct to use the binomial PDF, to answer the question "If the probability of getting heads is .5, then what are the chances of getting 4 heads in 5 flips?" This gives .15625, which is not the right P-value. The correct answer is 3/16, but how do I get this value? What probability distribution to I use to obtain this P-value?

For binomial(5, 1/2), they take p-value = P(4) + P(5) = (5/32) + (1/32) = 3/16, so they take p-value = P(4 or more heads).