SECTION 6.6 χ^2 and Goodness of Fit 409
In general, experiments of the above type are calledmultinomial
experiments, which generalize in a natural way the familiar bino-
mial experiments. A multinomial experiment results in a number of
occurrences in each of possibly many categories; the binomial experi-
ment results in a number of occurrences in each of only two categories.
The result of a multinomial experiment is typically summarized in a
one-way table, the table on page 405 being a good example. Theχ^2
test used to test the null hypothesis regarding the individual category
probabilities is often referred to as atest for homogeneity.
The TI-83 calculators are quite adept at a variety of tests of hy-
potheses; however, they don’t have a built-in code to test homogeneity
hypotheses.^30 (They do, however, have a built-in code to test for in-
dependence, which we’ll consider below.) At any rate, here’s a simple
code which will test for homogeneity. Preparatory to running this pro-
gram, one puts into list variableL 1 the observed counts and into list
variableL 2 the expected counts. For the problem of the putative fair
die, the entries 33, 40, 39, 28, 36, 24 are placed inL 1 and the entry
200 /6 = 33.333 is placed into the first six entries ofL 2.
The following simple code will finish the job:
(^30) This was remedied on the TI-84s.