Let us reconsider the problem presented in Example 11.2b. A simulation study yielded the result

and so the critical value should be 9.52381, which is remarkably close to χ2 .05,4 = 9.488 given as the critical value by the chi-square approximation. This is most interesting since the rule of thumb for when the chi-square approximation can be applied—namely, that each npi ≥ 1 and at least 80 percent of the npi exceed 5 — does not apply, thus raising the possibility that it is rather conservative. ■
Program 11.2.2 can be utilized to determine the p-value.
To obtain more information as to how well the chi-square approximation performs, consider the following example.

PHOT 9.52381} = .95