Hypothesis Testing with Two Samples

Summary :

This chapter extends hypothesis testing to comparisons between two groups, using business examples such as night-shift versus day-shift productivity and the investment returns of two different strategies. It distinguishes independent groups from matched pairs and covers testing two population means and two population proportions under each design.

Independent groups versus matched pairs

Comparing two groups requires first classifying them as independent, where sample values from one population are unrelated to those from the other, or as matched pairs, where the two samples are dependent, and the chapter uses this distinction to determine which testing method and which parameter, means or proportions, applies.

Comparing two independent population means

The comparison of two independent population means is presented as a common business question, illustrated with whether the night shift is less productive than the day shift or whether one investment strategy's returns differ from another's, framing the two-sample mean comparison as a natural extension of the one-sample methods covered earlier.

Comparing two proportions and paired samples

Beyond comparing means, the chapter covers hypothesis tests for two population proportions, useful for comparing rates such as production efficiency under different management styles, and for matched or paired samples, where the same subjects or units are measured under two conditions and the pairing itself must be accounted for in the test.