Final answer:
The correct approach when sigma is unknown for constructing a confidence interval or a hypothesis test for a single population mean is to use the T-distribution, with the sample standard deviation serving as an estimator for the unknown population standard deviation, assuming normality and independence.
Step-by-step explanation:
When sigma is unknown and you are constructing a confidence interval or performing a hypothesis test for a single population mean, you should use the T-distribution. The correct answer to the original question is A) T-distribution; using sample standard deviation (s); assumptions include normality and independence. The use of the T-distribution is appropriate when working with a sample where the population standard deviation (σ) is not known. Instead, the sample standard deviation (s) is used as an estimator for the unknown population standard deviation (σ). The assumptions for using the T-distribution include that the data come from a simple random sample, the population that the sample is taken from is normally distributed, or if not, the sample size is large enough for the Central Limit Theorem to ensure the distribution of the sample mean is approximately normal.