# Equiprobable model for Pearson's goodness-of-fit method.

There is a very long introduction to this problem. I can provide this if needed but for now I will stick with the actual question.

"A question of interest to the researchers was whether there were any "nonrandom features" about the location of the 296 sites of potential importance for reproduction of a certain genome. Strands of the DNA have almost 230 thousand bases. One way to study this question is to divide the locations into 20 ranges, to count the number of potential important sites in each range, and to determine if the counts are consistent with an equiprobable model "

(A table is then given that describes the 20 location groups and number of sites associated with each. The first, for example, is location group: $0<X<11500$, number of sites: $12$)

"Use Pearson's goodness-of-fit method to determine if the potentially important sites are randomly distributed over the genome in the sense given above (that is, to determine if the counts in the table above are consistent with an equiprobable model)."

I understand how to use Pearson's goodness-of-fit model but my professor never explained what an equiprobable model is. I am therefore unsure how to find the probability of each range to be used in calculations for the goodness-of-fit. Furthermore, I am unsure about what $n$ would be. Is it $20$ or is it $296$ or is it $23000$?

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The equiprobable model is that there are an equal number of sites in each location group, i.e., $296/20=14.8$ sites per group, and, assuming that you are using the $\chi^2$ test, you should use a $\chi^2$ statistic with one less degree of freedom than the number of groups, i.e.,$19$ degrees of freedom.