Which theorem can be used to compute confidence intervals around the population mean from a single simple mean?

The Central Limit Theorem is crucial for computing confidence intervals around the population mean based on a single sample mean. This theorem states that, given a sufficiently large sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution from which the sample is drawn.

This property is particularly important because it allows researchers to use the normal distribution to approximate the behavior of the sample mean. When you take a sample and calculate its mean, the Central Limit Theorem assures you that as long as your sample size is large enough (commonly n ≥ 30 is used as a rule of thumb), the sampling distribution of that mean will be approximately normally distributed.

Consequently, you can then apply the normal distribution to calculate confidence intervals for the population mean. This is done by determining the standard error of the sample mean and using it to define the range within which the true population mean is expected to lie, based on the desired confidence level.