Question
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$5.00 goodness-of-fit test, etc
- From Mathematics: Statistics
- Closed, but you can still post tutorials
- Due on Nov. 30, 2008
- Asked on Nov 28, 2008 at 9:57:13PM
Q:A student of architecture takes trips to France to make visits to the 92 cathedrals of the Roman Cantolic Church in France. The Church in France is divided into 15 provinces (exluding overseas territories. During his trip he visits 57 different cathedrals and the number of visited cathedrals by province are given below in the table. 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 province of France.
Another hypothesis is that the probability that a cathedral in a province is visited by the student is proportional to the number of cathedrals in that province of France. Show that Ei, the expected number of cathedrals visited by the student, in th ith province is given by
Ei=(ri times the summation nj from j=1 to k)/rj from j=1 to k, for 1<=i<=k
(note:above ri means r suscript i same applies to nj and rj)
n subscript i is the number of cahedrals visited by the student in the ith province, r subscript i is the number of cathedrals in the ith province and k is the number of provinces. Hence use a chi square goodness of fit test to test this other hypothesis.
Province(i).......1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 total
number visited(ni)4 5 1 0 1 0 1 4 8 5 6 7 6 5 4 57
No.in Province(ri)8 5 3 4 4 8 7 5 8 5 7 9 6 8 5 92
