Rather than eyeballing a histogram or a continuous probability distribution, let's look at the Table 30.1 that tells us the value that corresponds to various -values and various degrees of freedom. Our value of 6.67 with two degrees of freedom corresponds to a -value between 0.05 and 0.025. (A statistics calculator gives us the more precise -value of 0.0356.) Notice that if there were three degrees of freedom, then the -value would be between 0.10 and 0.05. These -values mirror what we determined earlier with the simulation histograms.
Table 30.1 Chi-squared table.