Study Notes
Hypothesis testing is a statistical method used to decide whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis. It involves setting up a null hypothesis (H₀) and an alternative hypothesis (H₁), then using sample data to determine if H₀ can be rejected at a given significance level.
- Null Hypothesis (H₀) — a statement that there is no effect or difference, often represented by an equality. Example: H₀: p = 0.5, meaning the probability of heads is 0.5.
- Alternative Hypothesis (H₁) — a statement that contradicts the null hypothesis, indicating an effect or difference. Example: H₁: p ≠ 0.5, meaning the probability of heads is not 0.5.
- Significance Level — the probability of rejecting the null hypothesis when it is true, often set at 5% or 1%. Example: A 5% significance level means there is a 5% risk of concluding that a difference exists when there is none.
- Type I Error — rejecting the null hypothesis when it is true. Example: Concluding a coin is biased when it is actually fair.
- Type II Error — failing to reject the null hypothesis when it is false. Example: Concluding a coin is fair when it is actually biased.
Exam Tips
Key Definitions to Remember
- Null Hypothesis (H₀)
- Alternative Hypothesis (H₁)
- Significance Level
- Type I Error
- Type II Error
Common Confusions
- Confusing Type I and Type II errors
- Misunderstanding the significance level as the probability of the null hypothesis being true
Typical Exam Questions
- What is the null hypothesis in this scenario? Identify H₀ based on the given context.
- How do you determine if a result is statistically significant? Compare the p-value to the significance level.
- What is the probability of a Type I error? It is equal to the significance level.
What Examiners Usually Test
- Ability to formulate null and alternative hypotheses
- Understanding of significance levels and critical regions
- Calculation and interpretation of Type I and Type II errors