- 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?
Recall the scenario: Suppose that you are playing a game with your friend that involves flipping a coin. Each round consists of flipping the coin [latex]10[/latex] times. In one round of play, your friend gets [latex]8[/latex] heads out of the [latex]10[/latex] total flips.
If you wanted to claim that your friend was indeed cheating, you would need to produce evidence in order to prove that their coin was not fair. Statistics is a very useful tool in this scenario and can be used to test these kinds of hypotheses.
hypothesis test
In a statistical hypothesis test:
- The null hypothesis, [latex]H_{0}[/latex], is what we assume to be true to begin with. It is often a statement of no change from the previous value or from what is expected.
[latex]H_0: p = \text{null value}[/latex]
- The alternative hypothesis, [latex]H_{A}[/latex], is what we consider to be plausible if the null hypothesis is false.
[latex]H_{A}: p>\text{null value}[/latex]
[latex]H_{A}: p<\text{null value}[/latex]
[latex]H_{A}: p \neq \text{null value}[/latex]
- The evidence used is probability. The statistical evidence that we gather is always evidence in support of the alternative hypothesis and against the null hypothesis. We ask ourselves the question, “Do we have enough evidence to reject the null hypothesis?”
- The outcomes of the hypothesis test are either:
- We reject the null hypothesis (we have gathered enough evidence).
- We fail to reject the null hypothesis (we have not gathered sufficient evidence, so we cannot reject the starting assumption).
Before we can conduct a hypothesis test and calculate the probability, we need to check if the conditions for the hypothesis test have been met.