Which of the following is not a condition that must be checked when estimating the mean $\mu$ of a population?

• A. The sample data are randomly selected from the population.
• B. The observations are independent of each other.
• C. The population standard deviation $\sigma$ is known.
• D. The sample size is sufficiently large or the population is approximately normal.

Answer: (C)

Verified step by step guidance

1. Understand that when estimating the mean of a population, certain conditions must be met to ensure the validity of the inference.
2. Identify the common conditions: (1) The sample data are randomly selected from the population, ensuring representativeness; (2) The observations are independent, meaning one observation does not influence another; (3) The sample size is sufficiently large or the population distribution is approximately normal, which allows the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.
3. Recognize that knowing the population standard deviation is not a necessary condition for estimating the population mean; it is relevant when constructing confidence intervals or conducting hypothesis tests under certain methods, but not a fundamental condition for estimation itself.
4. Compare each given option against these conditions to determine which one is not required as a condition for estimating the mean.
5. Conclude that the condition 'The population standard deviation is known' is not a required condition for estimating the population mean.