In order to make statistical inferences when testing a population mean, which of the following conditions must typically be met?

• A. The population must always be bimodal.
• B. The sample size must always be less than $30$.
• C. The sample should be randomly selected from the population.
• D. The population standard deviation must always be known.

Answer: (C)

Verified step by step guidance

1. Understand that when testing a population mean, certain conditions ensure the validity of the inference, such as the sample representing the population well.
2. Recognize that the sample should be randomly selected to avoid bias and to ensure that the sample is representative of the population.
3. Know that the population does not need to be bimodal; in fact, normality or approximate normality is often assumed, especially for small samples.
4. Be aware that the sample size does not always have to be less than 30; larger samples can be used, and the Central Limit Theorem helps with normality assumptions for large samples.
5. Understand that the population standard deviation does not always have to be known; if it is unknown, we typically use the sample standard deviation and a t-distribution for inference.