๐ Topic Summary
Hypothesis testing is a crucial part of statistical inference, allowing us to make decisions or draw conclusions about a population based on sample data. We formulate a null hypothesis (a statement of no effect or no difference) and an alternative hypothesis (the statement we are trying to find evidence for). We then collect data, calculate a test statistic, and determine the p-value, which indicates the probability of observing the obtained results (or more extreme results) if the null hypothesis were true. Based on the p-value and a chosen significance level (alpha), we decide whether to reject or fail to reject the null hypothesis. Keep in mind that failing to reject the null hypothesis doesn't prove it's true; it simply means we don't have enough evidence to reject it.
In essence, hypothesis testing provides a structured way to evaluate evidence and make informed decisions in the face of uncertainty. These worksheets help you to practice applying these concepts.
๐ง Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Null Hypothesis |
A. The probability of observing the obtained results (or more extreme) if the null hypothesis is true. |
| 2. Alternative Hypothesis |
B. The threshold for determining statistical significance. |
| 3. P-value |
C. A statement of no effect or no difference. |
| 4. Significance Level (alpha) |
D. The hypothesis we are trying to find evidence for. |
| 5. Test Statistic |
E. A number calculated from sample data used to evaluate the null hypothesis. |
Answer Key: 1-C, 2-D, 3-A, 4-B, 5-E
๐ Part B: Fill in the Blanks
Complete the following paragraph using the words: reject, significance level, null hypothesis, p-value, alternative hypothesis.
In hypothesis testing, we start by assuming the ___________ is true. We then calculate a ___________ from our data. If this value is less than our predetermined ___________, we ___________ the null hypothesis in favor of the __________.
Answer: null hypothesis, p-value, significance level, reject, alternative hypothesis.
๐ค Part C: Critical Thinking
Explain, in your own words, the difference between a Type I error and a Type II error in hypothesis testing. Provide an example of each.
(Example Answer: A Type I error occurs when we reject the null hypothesis when it is actually true (false positive). For example, concluding a drug is effective when it isn't. A Type II error occurs when we fail to reject the null hypothesis when it is false (false negative). For example, failing to find a drug effective when it actually is.)
