SOLUTION: aren't we suppose to divide p=0.5 by 2. since it is a two tailed test. i keep getting the wrong answer please help!! We have a coin and we would like to determine whether or not t

Question 677814: aren't we suppose to divide p=0.5 by 2. since it is a two tailed test. i keep getting the wrong answer please help!!
We have a coin and we would like to determine whether or not the coin is fair (i.e., whether the probability p of the coin landing on Heads differs from 0.5). We will flip the coin 20 times and conduct a hypothesis test of H0: p = 0.5 vs. Ha: p cannot equal to 0.5. Let X be the number of Heads that are flipped. We decide to reject the null hypothesis if X<= 4 or X>= 16.
(a) What is the probability of making a Type I Error? i got 0.1704. i dont know why i got it wrong.
(b) What is the probability of making a Type II Error if the true probability of Heads for this coin is actually 0.25? i got 0.4148. for this answer too. i do not know why i got it wrong.
please help!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
We have a coin and we would like to determine whether or not the coin is fair (i.e., whether the probability p of the coin landing on Heads differs from 0.5). We will flip the coin 20 times and conduct a hypothesis test of H0: p = 0.5 vs. Ha: p cannot equal to 0.5. Let X be the number of Heads that are flipped. We decide to reject the null hypothesis if X<= 4 or X>= 16.
(a) What is the probability of making a Type I Error? i got 0.1704. i dont know why i got it wrong.
Comment: The prob of a Type I Error is the probability of rejecting Ho.
P(x <=4) = binomcdf(20,1/2,4) = 0.0059
P(x >=16) = 1 - binomcdf(20,1/2,15) = 0.0059
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So P(Type I Error) = 2*0.0059 = 0.0118
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(b) What is the probability of making a Type II Error if the true probability of Heads for this coin is actually 0.25? i got 0.4148. for this answer too. i do not know why i got it wrong.
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Comment: The prob of Type II Error is the prob of not rejecting Ho.
P(4< x <16) = binomcdf(20,0.25,15)-binomcdf(20,0.25,4) = 0.5852
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Cheers,
Stan H.

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