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Someone flips a coin 12 times to decide whether or not the coin is "fair", i.e., if heads and tails come up an equal amount of times. Give all the elements of a hypothesis test: assumptions, hypotheses, rejection rule including test statistic

Someone flips a coin 12 times to decide whether or not the coin is "fair", i.e., if heads and tails come up an equal amount of times. Give all the elements of a hypothesis test: assumptions, hypotheses, rejection rule including test statistic

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Someone flips a coin 12 times to decide whether or not the coin is "fair", i.e., if heads and tails come up an equal amount of times. Give all the elements of a hypothesis test: assumptions, hypotheses, rejection rule including test statistic. If the coin were fair, how often would the test mistakenly decide otherwise if repeated many times? If the coin was unbalanced, i.e. coming up heads 75% of the time and tails 25% of the time, how often would the test mistakenly decide the coin was fair, if repeated many times? What error probabilities do you find here?

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Isn't the n too small for a normal approximation? Should the test statistic follow the t-distribution instead of z?

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