- Write a null and alternative hypothesis for a hypothesis test.
- Decide if a sample statistic provides enough evidence to reject the null hypothesis.
Is it fair?
In your experiment of [latex]20[/latex] coin flips, you assumed your friend’s coin is fair, and that assumption was used to calculate the probability of obtaining [latex]17[/latex] or more heads. The probability of [latex]0.0013[/latex] given in the previous question is the probability of obtaining [latex]17[/latex] or more heads out of [latex]20[/latex] flips if the coin is fair, and this low probability is evidence that the coin is not fair.
Note that no matter what probability you obtain, even if it is a high probability, it is not evidence that the coin is fair. This is because fairness was already the given assumption, and the probability was computed using the assumption that the coin is fair. If we assume something is true, we can’t use that assumption to prove that it’s true (that would be using circular logic). From our sample of coin flips, we either get enough evidence to say the coin is weighted or we don’t.
In hypothesis-testing language, we either get enough evidence to reject the null hypothesis or we don’t.
- When we don’t get enough evidence to reject the null hypothesis, we fail to reject the null hypothesis.
- NEVER accept the null hypothesis! This is because that was already our assumption to begin with.