Which of the following lists the requirements that must be met to perform a $\chi ²$ goodness-of-fit test?

• A. The data must be categorical, the expected frequency for each category should be at least $5$, and the observations must be independent.
• B. The data must be continuous, the expected frequency for each category should be at least $10$, and the categories must be mutually exclusive.
• C. The data must be ordinal, the expected frequency for each category should be less than $5$, and the observations must be dependent.
• D. The data must be numerical, the sample size must be less than $30$, and the categories must overlap.

Answer: (A)

Verified step by step guidance

1. Understand that the chi-square goodness-of-fit test is used to determine if observed categorical data fits a specific expected distribution.
2. Identify that the data must be categorical because the test compares frequencies across categories, not numerical measurements.
3. Recognize that the expected frequency for each category should be at least 5 to ensure the chi-square approximation to the distribution is valid.
4. Ensure that the observations are independent, meaning the occurrence of one observation does not affect another, which is crucial for the validity of the test.
5. Confirm that categories are mutually exclusive and collectively exhaustive, so each observation fits into one and only one category.