You 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.

Question

Suppose you decide to flip a coin 100 times.

a. What conclusion would you be likely to draw if you observed 95 heads?
b. What conclusion would you be likely to draw if you observed 55 heads?

Answer 1

a - either you've just seen something that's phenomenally unlikely, or the coin's owner isn't being truthful about the fairness of the coin.

b - you've just seen something that's consistent with the coin's owner's pronouncement that the coin is fair. (Not that that means it definitely IS fair: it's just that you don't have enough evidence to conclude that it isn't.)

I suspect you're about to be introduced to the concept of the so-called "null hypothesis", which in this instance is that the coin is fair, i.e. that heads and tails are equally likely to occur. When you do an experiment, either you get a result which is consistent with your null hypothesis, or you get a result which is so unlikely if the nullhypothesis is true that you're forced to throw the null hypothesis away. Your two questions are examples of that process.

Answer 2

Thanks so much for the reply!

Answer 3

You 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?
c. What is the parameter?
e. What is the statistic?
f. Describe briefly how statistical inference can be used to test the claim.