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For example, suppose there are four entrances to a building. You want to know if the four entrances are equally used. You observe 400 people entering the building on a random basis:

Goodness Of Fit

If the entrances are equally utilized, we would expect each entrance to be used approximately 25% of the time. Is the difference shown above statistically significant?

The purpose of a chi-square goodness-of-fit test is to compare an observed distribution to an expected distribution.  

H0: pM = pB = pS1 = pS2

H1: The proportions are not all equal.

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