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Chi square goodness of fit test

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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.

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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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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 ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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