Which of the following is not a requirement to conduct a $\chi -\mathrm{square}$ goodness-of-fit test?

• A. The expected frequency for each category should be at least $5$.
• B. The data must be obtained from a random sample.
• C. The population standard deviation must be known.
• D. The observations must be independent of each other.

Answer: (C)

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 specified distribution.
2. Recall the key requirements for conducting a chi-square goodness-of-fit test: (1) The data must come from a random sample, (2) The observations must be independent, and (3) The expected frequency for each category should be at least 5 to ensure the validity of the chi-square approximation.
3. Recognize that the population standard deviation is not a requirement for the chi-square goodness-of-fit test because this test deals with categorical data and frequencies, not means or variances of a numerical population.
4. Compare each given option against these requirements to identify which one does not belong as a necessary condition.
5. Conclude that the statement 'The population standard deviation must be known' is not a requirement for conducting a chi-square goodness-of-fit test.