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Question

A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?

 

Wouldn't the answer be:

You can conclude with 95% certainty that his abilities lie between the two endpoints of the interval. Each time the coin is flipped there is a 50/50 outcome.

Answer 1

If the coin is fair you would expect the probability to be 1/2 but the question is not asking that.

 

If the person correctly predicted the outcome in 16 out of 25 flips you want to calculate a 95% confidence interval based on that proportion.

 

i.e 16/25 +- 1.96(sqroot(pq/n))

 

p= 16/25   q=9/25   n=25.

 

 

Let me know if you understand.