Inference about a population mean when the standard deviation is. Confidence interval estimator and test statistic derived from sampling distribution of the sample with mean and sigma known. If population mean is unknown, then so is population standard deviation: substitute sample standard deviation s in place of unknown population std. dev, result called t-statistic; called student t distribution . When pop std. dev is unknown and pop is normal, test statistic for testing hypotheses about the mean is t-statistic formula : defined as student t distributed with v = n 1 degrees of freedom. For small populations, must adjust test statistic and interval estimator using finite pop correction factor. Populations large relative to sample size; ignore correction factor (20 times larger) Finite populations allow for use of confidence interval estimator of the mean to produce confidence interval estimator of population total: multiply lcl and ucl of estimate of mean by population size.