Which of the following is not a requirement to conduct a goodness-of-fit test?

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

Answer: (D)

Verified step by step guidance

1. Understand that a goodness-of-fit test is used to determine if observed categorical data matches an expected distribution.
2. Recall the key assumptions for conducting a goodness-of-fit test: observations must be independent, data should come from a random sample, and expected frequencies for each category should be sufficiently large (usually at least 5).
3. Recognize that the population standard deviation is not a requirement for a goodness-of-fit test because this test deals with categorical data and frequencies, not means or variances.
4. Compare each given option against these assumptions to identify which one does not belong as a requirement.
5. Conclude that the statement 'The population standard deviation must be known' is not a requirement for conducting a goodness-of-fit test.