Which of the following best describes the purpose of the $\chi ²$ goodness of fit test in statistics?

• A. It determines if there is a linear relationship between two quantitative variables.
• B. It tests whether the observed categorical data distribution matches an expected distribution.
• C. It measures the strength and direction of association between two ordinal variables.
• D. It compares the means of two independent groups to see if they are significantly different.

Answer: (B)

Verified step by step guidance

1. Understand that the chi-square goodness of fit test is used to compare observed categorical data to an expected distribution to see if they differ significantly.
2. Recognize that this test is not designed to analyze relationships between quantitative variables or compare means between groups.
3. Recall that the test calculates a chi-square statistic using the formula: \(\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}\), where \(O_i\) is the observed frequency and \(E_i\) is the expected frequency for category \(i\).
4. Interpret the test result by comparing the calculated chi-square statistic to a critical value from the chi-square distribution with appropriate degrees of freedom, which is usually the number of categories minus one.
5. Conclude whether the observed data fits the expected distribution based on whether the chi-square statistic exceeds the critical value, indicating a significant difference or not.