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# Chi square goodness of fit test

Please see the attached file for full problem description.

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A student of architecture takes a trip to France to make visits to the 92 cathedrals of the Roman Catholic Church in France. France is divided into 9 regions (excluding overseas territories). During his trips he visits 45 different cathedrals and the number of visited cathedrals by region is given in the table below.

Use a chi square goodness of fit test to test the hypothesis that a cathedral visited by the student is equally likely to be any region of France.

An alternative hypothesis is that the probability that a cathedral in a region is visited by the student is proportional to the number of cathedrals in that region of France. Show that , the expected number of cathedrals visited by the student in the ith region, is given by

, for ,

Where , is the number of cathedrals visited by the student in the ith region, , is the number of cathedrals in the ith region and k is the number of regions. Hence use a chi square goodness of fit test to test this alternative hypothesis.

#### Solution Summary

This shows how to use a chi square goodness of fit test to test the hypothesis that a cathedral visited by the student is equally likely to be any region of France.

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