EXAMPLE 16.6 Loss of Product Value

vitc

Food products are often enriched with vitamins and other supplements. Does the level of a supplement decline over time so that the user receives less than the manufacturer intended? Here are data on the vitamin C levels (milligrams per 100 grams) in wheat soy blend, a flour-like product supplied by international aid programs mainly for feeding children. The same nine bags of blend were measured at the factory and five months later in Haiti.10

Bag 1 2 3 4 5 6 7 8 9
Factory 45 32 47 40 38 41 37 52 37
Haiti 38 40 35 38 34 35 38 38 40
Difference 7 −8 12 2 4 6 −1 14 −3

We suspect that vitamin C levels are generally higher at the factory than they are five months later. We would like to test the hypotheses

  • : vitamin C has the same distribution at both times
  • : vitamin C is systematically higher at the factory

Because these are matched pairs data, we base our inference on the differences.