📚 Topic Summary
The Chi-Square Goodness-of-Fit test is a statistical tool used to determine if observed sample data matches an expected distribution. In simpler terms, it helps us figure out if our data 'fits' a particular pattern or theory. We compare the actual (observed) frequencies with the frequencies we'd expect if our theory was correct. A large difference between observed and expected frequencies suggests that our theory might not be a good fit for the data.
This test is extremely useful in various fields like genetics, marketing, and social sciences. By calculating a chi-square statistic and comparing it to a critical value (or using a p-value), we can make a decision about whether to reject our null hypothesis (the hypothesis that there is no significant difference between observed and expected values).
🗂️ Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Observed Frequency |
A. The expected counts if the null hypothesis is true. |
| 2. Expected Frequency |
B. A statement that there is no significant difference between observed and expected values. |
| 3. Null Hypothesis |
C. A threshold used to determine statistical significance. |
| 4. Significance Level |
D. The counts actually obtained in a sample. |
| 5. Chi-Square Statistic |
E. A measure of the difference between observed and expected frequencies. |
✍️ Part B: Fill in the Blanks
The Chi-Square Goodness-of-Fit test is used to determine if a sample data fits a ________ distribution. We compare ________ frequencies with ________ frequencies. The formula for the Chi-Square statistic is $ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} $, where $O_i$ represents the ________ frequency and $E_i$ represents the ________ frequency.
🤔 Part C: Critical Thinking
Explain a real-world scenario where a Chi-Square Goodness-of-Fit test would be useful. Be specific about the hypothesis being tested and the data that would be collected.