Study Notes
Hypothesis testing is a method used to determine if there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis. It involves setting a significance level and identifying critical values to decide whether to accept or reject the null hypothesis.
- Null Hypothesis (H₀) — A statement that there is no effect or difference, often representing a default position. Example: In a coin toss, H₀ might state that the coin is fair.
- Alternative Hypothesis (H₁) — A statement that contradicts the null hypothesis, indicating an effect or difference. Example: In a coin toss, H₁ might state that the coin is biased.
- Significance Level — The probability of rejecting the null hypothesis when it is true, often set at 5% or 10%. Example: A 5% significance level means there is a 5% risk of concluding that a difference exists when there is none.
- Critical Region — The range of values for which the null hypothesis is rejected. Example: If more than 80 heads are observed in 100 coin tosses, the null hypothesis might be rejected.
- One-tailed Test — A hypothesis test where the critical region is in one tail of the distribution. Example: Testing if a coin is biased towards heads.
- Two-tailed Test — A hypothesis test where the critical region is in both tails of the distribution. Example: Testing if a coin is biased in either direction.
Exam Tips
Key Definitions to Remember
- Null Hypothesis (H₀)
- Alternative Hypothesis (H₁)
- Significance Level
- Critical Region
- One-tailed Test
- Two-tailed Test
Common Confusions
- Confusing the null hypothesis with the alternative hypothesis
- Misinterpreting the significance level as the probability of the null hypothesis being true
Typical Exam Questions
- What is the null hypothesis in a coin toss experiment? The null hypothesis is that the coin is fair.
- How do you determine the critical value in a hypothesis test? By using the significance level and distribution table.
- What is the difference between a one-tailed and a two-tailed test? A one-tailed test checks for an effect in one direction, while a two-tailed test checks in both directions.
What Examiners Usually Test
- Understanding of hypothesis testing terminology
- Ability to set up and interpret hypothesis tests
- Correct use of significance levels and critical values