Statistics for Business: Decision Making and Analysis, 3rd Edition

17.2 Data for Comparisons

Let’s frame the comparison between two diets as a test of the difference between two populations. Chapter 16 introduced hypothesis tests as a method to demonstrate profitability beyond a reasonable doubt. Rejecting the null hypothesis H₀ of no change or status quo implies that the alternative has demonstrated itself to be more profitable than an economic threshold at the chosen level of significance, usually α = 0.05. The same framework applies to comparisons between two populations.

In order to state the hypotheses, we need some notation. Because we have two populations, symbols for parameters and statistics such as μ and $\overline{x}$ must identify the population. For this example, the subscript A identifies parameters and statistics ...