Which of the following is not a requirement for testing means in hypothesis testing?

• A. The population standard deviation must be known
• B. The sample size must always be greater than $100$
• C. The sample must be randomly selected
• D. The data should be approximately normally distributed if the sample size is small

Answer: (B)

Verified step by step guidance

1. Understand the context of hypothesis testing for means, which often involves assumptions about the population and sample to ensure valid results.
2. Recall that one common requirement is that the population standard deviation must be known when using a z-test for means, or unknown when using a t-test.
3. Recognize that the sample must be randomly selected to avoid bias and ensure the sample represents the population.
4. Note that if the sample size is small, the data should be approximately normally distributed to satisfy the assumptions of the test.
5. Identify that there is no strict requirement that the sample size must always be greater than 100; smaller samples can be used if other assumptions are met, making this the incorrect statement.