What is Statistical Hypothesis Testing? Core Concepts Explained for University Students

📚 Quick Study Guide

🔍 Hypothesis testing is a method for testing a claim or hypothesis about a population parameter using data measured in a sample.
• 🧪 The null hypothesis ($H_0$) is a statement of no effect or no difference. It's what we try to disprove.
• 📊 The alternative hypothesis ($H_1$ or $H_a$) is a statement that contradicts the null hypothesis. It's what we're trying to prove.
• 📈 A test statistic is a value calculated from sample data that is used to determine whether to reject the null hypothesis. Examples include z-scores, t-scores, and chi-square values.
• 📉 The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true.
• 🤔 Significance level ($\alpha$) is the probability of rejecting the null hypothesis when it is true (Type I error). Common values are 0.05 and 0.01.
• ✅ Decision Rule: If the p-value is less than or equal to the significance level, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
• 💡Type I Error: Rejecting the null hypothesis when it is true (false positive).
• ⛔ Type II Error: Failing to reject the null hypothesis when it is false (false negative).

Practice Quiz

1. Which of the following best describes the null hypothesis?

   1. A statement that there is a significant difference between two populations.
   2. A statement that there is no effect or no difference.
   3. A statement that the sample data is biased.
   4. A statement that the experiment is poorly designed.

2. What does the p-value represent in hypothesis testing?

   1. The probability that the null hypothesis is true.
   2. The probability of observing a test statistic as extreme as, or more extreme than, the one calculated if the null hypothesis is true.
   3. The probability of making a Type I error.
   4. The probability of making a Type II error.

3. What is the significance level ($\alpha$)?

   1. The probability of accepting the null hypothesis when it is false.
   2. The probability of rejecting the null hypothesis when it is false.
   3. The probability of rejecting the null hypothesis when it is true.
   4. The probability of accepting the null hypothesis when it is true.

4. If the p-value is 0.03 and the significance level is 0.05, what is the correct decision?

   1. Accept the null hypothesis.
   2. Reject the null hypothesis.
   3. Fail to reject the null hypothesis.
   4. Increase the sample size.

5. What is a Type I error?

   1. Failing to reject the null hypothesis when it is false.
   2. Rejecting the null hypothesis when it is true.
   3. Accepting the null hypothesis when it is true.
   4. Failing to reject the null hypothesis when it is true.

6. What is a Type II error?

   1. Rejecting the null hypothesis when it is true.
   2. Accepting the null hypothesis when it is true.
   3. Failing to reject the null hypothesis when it is false.
   4. Rejecting the null hypothesis when it is false.

7. In a one-tailed hypothesis test, the critical region is:

   1. Located on both sides of the distribution.
   2. Located only on one side of the distribution.
   3. Always centered around the mean.
   4. Irrelevant to the p-value.