A question

I went fly fishing with my friend John. We caught 14 fish. He was casting a Blue Bobber and caught six fish, and I was casting a Grimacing Willy and caught eight fish. I wondered, “Do Blue Bobbers tend to catch the same size fish as Grimacing Willies?”

To answer this question using the methods I have presented, I need to: (1) use as data the 14 fish we caught, measured by weight and structured into two groups based on which fly caught them; (2) use as a test statistic a number, calculated from the data, that sums up how much heavier are the fish caught on Blue Bobbers than the fish caught on Grimacing Willies; (3) hypothesize a specific probability mechanism that represents the hypothesis that weights of fish caught on Blue Bobbers are not different from weights of fish caught on Grimacing Willies; (4) put that mechanism in motion to compute a large number of data sets, each similar in structure to the one observed, but constituting a sample of the hypothesis; (5) from each data set calculate a value of the test statistic; (6) sort these values and report them as an estimate of the probability distribution predicted by the hypothesis that fish weights are not different; (7) see where in this predicted distribution the observed weight difference falls; and finally (8) decide whether the observed data seem to be consistent with the hypothesis.