Table of Contents
What Is Hypothesis Testing?
Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. You start with a null hypothesis (H0) that states there is no effect or difference, and an alternative hypothesis (H1) that states there is an effect.
The test calculates how likely the observed data would be if the null hypothesis were true. If this probability (p-value) is less than the significance level, you reject the null hypothesis in favor of the alternative.
Test Statistics
The z-test is used when the population standard deviation is known or the sample size is large (n ≥ 30). For smaller samples with unknown population SD, a t-test is more appropriate.
Steps in Hypothesis Testing
- State the null and alternative hypotheses.
- Choose the significance level (α).
- Calculate the test statistic.
- Find the p-value or compare with critical value.
- Make a decision: reject or fail to reject H0.
Common Critical Values (z-test)
| α | Two-tailed | One-tailed |
|---|---|---|
| 0.10 | ±1.645 | 1.282 |
| 0.05 | ±1.960 | 1.645 |
| 0.01 | ±2.576 | 2.326 |
Frequently Asked Questions
What does the p-value mean?
The p-value is the probability of observing a test statistic as extreme as (or more extreme than) the one calculated, assuming the null hypothesis is true. A smaller p-value provides stronger evidence against H0.
What is Type I and Type II error?
Type I error (false positive) occurs when you reject a true null hypothesis. Its probability equals α. Type II error (false negative) occurs when you fail to reject a false null hypothesis.
When should I use a one-tailed vs two-tailed test?
Use a two-tailed test when you want to detect a difference in either direction. Use a one-tailed test when you only care about one direction, such as testing whether a mean is greater than a specific value.