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Hypothesis tests
Hypothesis testing is a formal procedure for using sample data to evaluate a claim about a population. We test a 'default' claim (the null hypothesis) against an alternative, and decide if our data provides enough evidence to reject the default.
Need to know
What you need to know
- **Null Hypothesis ($H_0$)**: Always includes an equality. E.g., $H_0: \mu = 100$.
- **Alternative Hypothesis ($H_1$)**: Includes an inequality. The form depends on the question.
- **One-tailed test**: Used for directional claims. Keywords: 'increase', 'decrease', 'more than', 'less than'. E.g., $H_1: \mu > 100$ or $H_1: \mu < 100$.
- **Two-tailed test**: Used for non-directional claims. Keywords: 'change', 'different from'. E.g., $H_1: \mu \neq 100$. For a two-tailed test, the significance level $\alpha$ is split equally between the two tails ($\alpha/2$ in each).
Explanation
Testing Claims with Data
- State the null hypothesis H₀ (the default or 'no change' claim) and the alternative H₁ (one-tailed for increase/decrease, two-tailed for 'change').
- A Type I error is rejecting a true H₀. A Type II error is failing to reject a false H₀. The significance level, α, is the probability of a Type I error.
- Calculate the test statistic from your sample data. Compare it to the critical value from tables, or find the p-value and compare it to the significance level α.
- Use a Z-test for the mean (Normal distribution or large sample) or for a proportion. If the test statistic is in the critical region (or p < α), reject H₀.