Discussion:
Q: 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 Ei, the expected number of cathedrals visited by the student in the ith region, is given by
Ei= ri Σj-1knj/ Σj-1krj 1 ≤ i ≤ k
Where ni, is the number of cathedrals visited by the student in the ith region, ri, 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.
|
Region (i)
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
Total
|
|
Number of visited (ni)
|
8
|
4
|
3
|
4
|
10
|
0
|
9
|
7
|
0
|
45
|
|
Number in region (ri)
|
8
|
8
|
10
|
13
|
10
|
11
|
12
|
11
|
9
|
92
|