- 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?
Suppose that you are playing a game with your friend that involves flipping a coin. What if you wanted to investigate whether the coin you and your friend are using in your game is fair?
When you are playing a game with your friend that involves flipping a coin, you have a baseline assumption when you start playing the game with your friend: the coin is fair. This assumption is called the null hypothesis.
Suppose in one round of play, your friend gets [latex]8[/latex] heads out of the [latex]10[/latex] total flips. Would you be surprised? Results like this may suggest that the coin is, in fact, not fair and tends to favor heads. This is what we call an alternative hypothesis.
In reality, the probability of flipping a coin and getting heads more than 8 times out of 10 is [latex]5.24\%[/latex]. Do you think the coin is fair?
null hypothesis
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 (e.g., we expect a coin to be fair).
- The null hypothesis, [latex]H_{0}[/latex], is always given in the form: [latex]\text{parameter} = \text{null value}[/latex].
- For proportion, our parameter is population proportion, denoted [latex]p[/latex], therefore our null hypothesis is [latex]H_0: p = \text{null value}[/latex]
alternative hypothesis
The alternative hypothesis, [latex]H_{A}[/latex], is what we consider to be plausible if the null hypothesis is false. It usually represents a change or difference from what the null hypothesis states, and we want to test if that difference is supported by evidence from a sample. The alternative hypothesis answers the question, “Do we think the actual parameter is larger than, smaller than, or just different from the null value, where the null value is the value specified in the null hypothesis?”
- The alternative hypothesis, [latex]H_{A}[/latex], is always given as an inequality:
- [latex]\text{parameter}>\text{null value}[/latex],
- [latex]\text{parameter}<\text{null value}[/latex], or
- [latex]\text{parameter} \neq \text{null value}[/latex].
- For a proportion, the alternative hypothesis can be:
- [latex]H_{A}: p>\text{null value}[/latex],
- [latex]H_{A}: p<\text{null value}[/latex], or
- [latex]H_{A}: p \neq \text{null value}[/latex].