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 standard deviation $\sigma$ is known.
• B. The sample is a simple random sample.
• C. The data are obtained independently.
• D. The population is normally distributed or the sample size is large.

Answer: (A)

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 using the t-test for a population mean: (1) The sample must be a simple random sample, (2) The data must be obtained independently, and (3) The population should be normally distributed or the sample size should be large enough for the Central Limit Theorem to apply.
3. Recognize that knowing the population standard deviation is not a requirement in this scenario; in fact, the t-test is specifically used because the population standard deviation is unknown.
4. Identify that the statement 'The population standard deviation is known' contradicts the premise of using the t-test and is therefore not a requirement for this test.
5. Conclude that the correct answer is the statement that the population standard deviation is known, as it is not a requirement when the population standard deviation is unknown.