Advertisements for Kellogg’s Raisin Bran indicate that there are two scoops of raisins in every box, and two plastic scoops, along with the words “Two scoops!”, appear prominently on the front of the box. Unfortunately, a scoop is a nonstandard unit of volume, so the prevalence of raisins in the cereal remains uncertain. Moreover, Kellogg’s Raisin Bran comes in 15-, 20-, and 25.5-ounce boxes, all of which bear the “Two scoops!” claim. This observation suggests two alternative hypotheses:
(A) Scoop size is independent of box size. In other words, the same scoops are used to add raisins to each box, regardless of box size, so that the number of raisins per box is constant.
(B) Scoop size is proportional to box size. In other words, larger scoops are used for the larger boxes so that the number of raisins per ounce of cereal remains constant.
In order to distinguish between these hypotheses, we counted the number of raisins in boxes of different sizes.
We obtained the following raisin counts in boxes of the indicated sizes:
15 oz: 201 (13.4 raisins/oz), 241 (16.1 raisins/oz)
20 oz: 381 (19.1 raisins/oz), 294 (14.7 raisins/oz)
25.5 oz: 308 (12.1 raisins/oz), 331 (13.0 raisins/oz)
In our sample of six boxes, there was a nearly two-fold range in the number of raisins per box (201 to 381). Since the number of raisins per box is not constant, we can reject Hypothesis A. The number of raisins per ounce is not constant either (range: 12.1 to 19.1), so we can reject Hypothesis B as well. Instead, the considerable variability in both raisins per box and raisins per ounce suggest some additional hypotheses to be tested by further work:
(C) Kellogg employees are poorly trained in the operation of the scoops.
(D) Kellogg factories are equipped with a very large number of scoops of different sizes such that no two scoops are alike.
(E) Kellogg allocates raisins via some stochastic process rather than with scoops.
If you like raisins, you should buy Kellogg’s Raisin Bran in 20-oz. boxes, which appear to contain the most raisins per ounce. If you dislike raisins, we recommend the 25.5-oz. boxes or, better yet, a raisin-free cereal.
To achieve truth in advertising and avoid lawsuits, The Kellogg Company should replace its misleading “Two scoops!” slogan with a statement listing both the mean number of scoops per box (presumably 2) and the standard deviation (roughly 0.4).
Our research was inspired by an episode of “Perfect Strangers” (Season 3, Episode 3; original air date October 14, 1987) in which Balki counts the number of raisins in a box of Raisin Puffs.