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You are going to flip a coin 12 times to decide whether or not it is “fair”—coming up “heads” and “tails” equally often. State all the elements of a hypothesis test: assumptions, hypotheses, rejection rule including test statistic, etc. (realizing the ? in this binomial is too small for a normal approximation).  Further, if the coin were fair, how often (if repeated many times) would your test mistakenly decide otherwise? If the coin was unbalanced, coming up “heads” 75% of the time and only 25% for tails, how often (if repeated many times) would your test mistakenly decide that the coin was fair? What error probabilities would you find here?

You are going to flip a coin 12 times to decide whether or not it is “fair”—coming up “heads” and “tails” equally often. State all the elements of a hypothesis test: assumptions, hypotheses, rejection rule including test statistic, etc. (realizing the ? in this binomial is too small for a normal approximation).  Further, if the coin were fair, how often (if repeated many times) would your test mistakenly decide otherwise? If the coin was unbalanced, coming up “heads” 75% of the time and only 25% for tails, how often (if repeated many times) would your test mistakenly decide that the coin was fair? What error probabilities would you find here?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 14CR
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You are going to flip a coin 12 times to decide whether or not it is “fair”—coming up “heads” and “tails”
equally often. State all the elements of a hypothesis test: assumptions, hypotheses, rejection rule including test statistic, etc. (realizing the ? in this binomial is too small for a normal approximation). 
Further, if the coin were fair, how often (if repeated many times) would your test mistakenly decide otherwise? If the coin was unbalanced, coming up “heads” 75% of the time and only 25% for tails, how often (if repeated many times) would your test mistakenly decide that the coin was fair? What error probabilities would you find here?

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