Which of the following is NOT a condition or assumption required for the one-sample t inference for the mean $\mu$ of a population?

• A. The population distribution is approximately normal or the sample size is large
• B. The population standard deviation $\sigma$ is known
• C. The data are a random sample from the population
• D. Observations are independent of each other

Answer: (B)

Verified step by step guidance

1. Understand that the one-sample t-test is used to make inferences about a population mean \( \mu \) when the population standard deviation \( \sigma \) is unknown.
2. Recall the key assumptions for the one-sample t-test: (1) The data come from a random sample or randomized experiment, (2) Observations are independent, and (3) The population distribution is approximately normal or the sample size is large enough for the Central Limit Theorem to apply.
3. Note that unlike the z-test, the one-sample t-test does NOT require the population standard deviation \( \sigma \) to be known; instead, it uses the sample standard deviation as an estimate.
4. Evaluate each given condition against these assumptions to identify which one is NOT required for the one-sample t-test.
5. Conclude that the condition 'The population standard deviation \( \sigma \) is known' is NOT an assumption for the one-sample t-test, making it the correct answer.