Which of the following is not a requirement for testing a claim about a population mean when the population standard deviation is not known?

• A. The population must be normally distributed or the sample size must be large.
• B. The sample data must be quantitative.
• C. The sample must be randomly selected from the population.
• D. The population standard deviation must be known.

Answer: (D)

Verified step by step guidance

1. Understand that when testing a claim about a population mean without knowing the population standard deviation, we typically use the t-distribution instead of the normal distribution.
2. Recall the key requirements for performing a t-test for a population mean: (1) the sample data must be quantitative, (2) the sample must be randomly selected from the population, and (3) the population should be approximately normally distributed or the sample size should be large enough for the Central Limit Theorem to apply.
3. Recognize that the population standard deviation being known is a requirement for using the z-test, not the t-test, so it is not a requirement when the population standard deviation is unknown.
4. Compare each given option against these requirements to identify which one does not belong as a requirement for the t-test scenario.
5. Conclude that the statement 'The population standard deviation must be known' is not a requirement for testing a claim about a population mean when the population standard deviation is unknown.