📚 Topic Summary
In hypothesis testing, the critical region (also called the rejection region) is a set of values for the test statistic for which the null hypothesis is rejected. In other words, these are the values that provide strong evidence against the null hypothesis. Identifying the critical region is crucial because it defines the threshold at which we decide whether to reject or fail to reject the null hypothesis.
The size of the critical region is determined by the significance level ($\alpha$), which represents the probability of rejecting the null hypothesis when it is actually true (Type I error). For example, a significance level of 0.05 means there's a 5% chance of incorrectly rejecting the null hypothesis.
🧠 Part A: Vocabulary
Match the terms with their correct definitions:
| Term |
Definition |
| 1. Null Hypothesis |
A. The probability of rejecting the null hypothesis when it is true. |
| 2. Alternative Hypothesis |
B. The range of values that leads to rejecting the null hypothesis. |
| 3. Significance Level ($\alpha$) |
C. A statement that there is no effect or no difference. |
| 4. Critical Region |
D. A statement that contradicts the null hypothesis. |
| 5. Test Statistic |
E. A value calculated from sample data used to determine whether to reject the null hypothesis. |
(Answers: 1-C, 2-D, 3-A, 4-B, 5-E)
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided:
(Words: reject, null hypothesis, significance level, critical region, alternative hypothesis)
In hypothesis testing, if the test statistic falls within the ________, we ________ the ________. This means we have enough evidence to support the ________ at the chosen ________.
(Answers: critical region, reject, null hypothesis, alternative hypothesis, significance level)
🤔 Part C: Critical Thinking
Explain, in your own words, why it is important to carefully choose the significance level ($\alpha$) before conducting a hypothesis test. What are the potential consequences of setting it too high or too low?