Summary
Statistical hypothesis testing is a method used to determine if there is enough evidence to reject a null hypothesis about a population parameter.
- Null Hypothesis (H₀) — a statement that there is no effect or no difference, often representing a default position. Example: The coin is not biased.
- Alternative Hypothesis (H₁) — a statement that contradicts the null hypothesis, indicating the presence of an effect or difference. Example: The coin is biased.
- Significance Level — the probability of rejecting the null hypothesis when it is true, often denoted by alpha (α). Example: A 5% significance level means there is a 5% risk of concluding that a difference exists when there is no actual difference.
- Critical Region — the set of values for which the null hypothesis is rejected. Example: If more than x heads are observed, the null hypothesis is rejected.
- Type I Error — rejecting the null hypothesis when it is true. Example: Concluding the coin is biased when it is not.
- Type II Error — failing to reject the null hypothesis when it is false. Example: Concluding the coin is not biased when it is.
- One-tailed Test — tests if a parameter is greater than or less than a certain value. Example: Testing if the mean is greater than a specified value.
- Two-tailed Test — tests if a parameter is different from a certain value. Example: Testing if the mean is not equal to a specified value.
Exam Tips
Key Definitions to Remember
- Null Hypothesis (H₀)
- Alternative Hypothesis (H₁)
- Significance Level
- Critical Region
- 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 the critical region? Use the significance level to find the critical values.
- What is the probability of a Type I error? It is equal to the significance level.
What Examiners Usually Test
- Understanding of hypothesis testing concepts
- Ability to set up and interpret null and alternative hypotheses
- Calculation and interpretation of significance levels and critical regions