Printable Chi-Square Goodness-of-Fit Practice Problems with Solutions

📚 Topic Summary

The Chi-Square Goodness-of-Fit test is a statistical tool used to determine if observed sample data fits a hypothesized distribution. In simpler terms, it checks if your data is what you expect it to be. The test compares observed frequencies (the actual data you collect) with expected frequencies (the values you anticipate based on a specific hypothesis). A large difference between observed and expected frequencies indicates a poor fit, suggesting that the hypothesized distribution is not a good model for the data. The test statistic, $\chi^2$, quantifies this difference.

Essentially, you're calculating how far off your real-world results are from your predicted results. If the difference is big enough (based on a predetermined significance level and degrees of freedom), you reject the idea that your prediction was accurate.

🧪 Part A: Vocabulary

Match the terms with their definitions:

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

1. Definition: A statement of no effect or no difference.
2. Definition: The categories that are free to vary in the calculation.
3. Definition: The sum of the squared differences between observed and expected values, divided by the expected values.
4. Definition: The actual count of occurrences in a sample.
5. Definition: The count of occurrences that would be expected under a specific distribution.

📝 Part B: Fill in the Blanks

The Chi-Square Goodness-of-Fit test is used to determine if a sample data fits a _________ distribution. It compares _________ frequencies with _________ frequencies. A large difference suggests a _________ fit, leading to a rejection of the _________.

🤔 Part C: Critical Thinking

Explain a real-world scenario where a Chi-Square Goodness-of-Fit test could be useful, and why it's important in that situation.