Goodness-of-Fit Test Assumptions and Interpretation Practice Quiz

📚 Topic Summary

The Goodness-of-Fit test helps determine if a sample data set matches a population with a specific distribution. We check assumptions to ensure the test is valid. These assumptions usually involve having a random sample, a sufficiently large sample size (expected counts ≥ 5), and independent observations. Interpretation involves comparing the calculated test statistic to a critical value from the chi-square distribution or examining the p-value. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, suggesting the data does not fit the hypothesized distribution. 🤔

This quiz will test your knowledge of these assumptions and your ability to interpret the results of a Goodness-of-Fit test. Good luck!🍀

🔤 Part A: Vocabulary

Match the following terms with their definitions:

1. Term: Chi-Square Statistic
2. Term: Null Hypothesis
3. Term: P-value
4. Term: Degrees of Freedom
5. Term: Expected Frequency

1. Definition: The number of independent pieces of information used to calculate a statistic.
2. Definition: A measure of the discrepancy between observed and expected frequencies.
3. Definition: The hypothesis that there is no significant difference between the observed and expected distributions.
4. Definition: The probability of obtaining results as extreme as, or more extreme than, the observed results, assuming the null hypothesis is true.
5. Definition: The frequency we would expect to see in a category if the null hypothesis were true.

✍️ Part B: Fill in the Blanks

The Goodness-of-Fit test is used to determine if a sample data set __________ a specified __________. One key assumption is that the __________ counts in each category should be sufficiently __________, generally at least __________. If the p-value is less than the significance level, we __________ the null hypothesis.

🤔 Part C: Critical Thinking

Explain why it's important to check the assumptions of a Goodness-of-Fit test before interpreting the results. What could happen if the assumptions are violated?