type 1 and type 2 errors hypothesis testing definition

📚 Quick Study Guide

• 🔍 Hypothesis Testing: A method for testing a claim or hypothesis about a population parameter using sample data.
• 🍎 Null Hypothesis (H₀): A statement of no effect or no difference. We aim to reject or fail to reject this.
• 🧪 Alternative Hypothesis (H₁): A statement that contradicts the null hypothesis. This is what we are trying to find evidence for.
• ⚠️ Type I Error (False Positive): Rejecting the null hypothesis when it is actually true. Represented by $\alpha$ (alpha).
• ⛔ Type II Error (False Negative): Failing to reject the null hypothesis when it is actually false. Represented by $\beta$ (beta).
• 📊 Significance Level ($\alpha$): The probability of making a Type I error. Commonly set at 0.05 (5%).
• 💪 Power (1 - $\beta$): The probability of correctly rejecting the null hypothesis when it is false.

Practice Quiz

1. Which of the following defines a Type I error?
   1. Rejecting the null hypothesis when it is true.
   2. Failing to reject the null hypothesis when it is false.
   3. Correctly rejecting the null hypothesis.
   4. Correctly failing to reject the null hypothesis.
2. What is the probability of committing a Type I error denoted by?
   1. $\beta$
   2. 1 - $\beta$
   3. $\alpha$
   4. 1 - $\alpha$
3. Which of the following defines a Type II error?
   1. Rejecting the null hypothesis when it is true.
   2. Failing to reject the null hypothesis when it is false.
   3. Correctly rejecting the null hypothesis.
   4. Correctly failing to reject the null hypothesis.
4. What is the probability of committing a Type II error denoted by?
   1. $\alpha$
   2. 1 - $\alpha$
   3. $\beta$
   4. 1 - $\beta$
5. The power of a test is defined as:
   1. The probability of rejecting a false null hypothesis.
   2. The probability of rejecting a true null hypothesis.
   3. The probability of failing to reject a false null hypothesis.
   4. The probability of failing to reject a true null hypothesis.
6. What is the relationship between power and the probability of a Type II error?
   1. Power = $\beta$
   2. Power = 1 + $\beta$
   3. Power = 1 - $\beta$
   4. Power = $\alpha$ + $\beta$
7. If the significance level ($\alpha$) is set to 0.05, this means:
   1. There is a 5% chance of committing a Type II error.
   2. There is a 5% chance of correctly failing to reject the null hypothesis.
   3. There is a 5% chance of committing a Type I error.
   4. There is a 95% chance of committing a Type I error.