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kathyp
ou are shown a coin that its owner says is fair in the sense that it will produce the same number of heads and tails when flipped a very large number of times. a. Describe an experiment to test this claim. b. What is the population in your experiment?
In this case, the common-sense approach is correct. Flip the coin a great many times. See if the resulting number of heads is close to 50%. This is classic 'Bernoulli trials' experiment, because there are two possible outcomes. The populations is the number of flips (events). Use the binomial distribution to determine how likely the result (or one more extreme) is to occur with a fair coin. For example, if you flip the coin 8 times and get heads once, sum the probability of getting zero or one heads in 8 tosses of a fair coin. (.035) So a fair coin would only give these results 3.5% of the time. (do you have this equation in your textbook?) A common acceptance criteria is 5%, so many would reject the coin as likely unfair. Experimenter must determine the appropriate number of tosses and the 'acceptance criteria' based on the amount of time available for testing and the impact of reaching a wrong conclusion. I hope this helps. There are different levels of detail that could be applied depending on what you are studying.