Unit 4: Inference for Quantitative Data: Means

Decide whether quantitative data require an independent two-sample t interval or a paired t interval, then interpret the difference correctly.

Sampling distribution of the sample mean guide with center, standard error, conditions, normal approximation, examples, and practice.

Estimate a population mean when the population standard deviation is unknown, using the sample standard deviation, a t critical value, and conditions that support the procedure.

Use a one sample t test to test a claim about one population mean when the population standard deviation is unknown. The procedure standardizes the distance between the sample mean and the null mean with s divided by the square root of n and evaluates that distance on a t distribution.

Choosing between a two-sample t test and a paired t test is a design decision before it is a calculation. Independent groups require a two-sample procedure; matched people, repeated measurements, or deliberately paired units require a one-sample t test on the within-pair differences.