📚 Topic Summary
The Chi-Square ($\chi^2$) distribution is a continuous probability distribution that arises frequently in hypothesis testing. It's particularly useful for analyzing categorical data. The shape of the Chi-Square distribution is determined by its degrees of freedom ($df$), which affect its skewness and overall form. Understanding the parameters, especially the degrees of freedom, is crucial for determining critical values. These critical values are used to assess the significance of statistical tests, helping us decide whether to reject or fail to reject a null hypothesis. Let's test your knowledge!
🧮 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Degrees of Freedom |
a. The value that defines the rejection region in a hypothesis test. |
| 2. Critical Value |
b. A measure of the difference between observed and expected frequencies. |
| 3. Chi-Square Statistic |
c. A distribution used to test the independence of categorical variables. |
| 4. Chi-Square Distribution |
d. The number of independent pieces of information used to calculate a statistic. |
| 5. Skewness |
e. A measure of the asymmetry of a probability distribution. |
(Match the numbers 1-5 to the letters a-e)
✍️ Part B: Fill in the Blanks
The Chi-Square distribution is a ______ distribution, meaning it is not symmetrical. Its shape depends on the ______. As the degrees of freedom increase, the distribution becomes more ______. Critical values are found using a Chi-Square table and a chosen ______ level.
🤔 Part C: Critical Thinking
Explain how the degrees of freedom influence the shape of the Chi-Square distribution and why this is important when conducting a hypothesis test.