5 A school management team oversees 11 different schools.
The school management team allows each student in the schools to choose one enrichment activity from 11 possible activities. The school management team count the number of students in each school choosing each of the possible activities. They then conduct a \(\chi ^ { 2 }\)-test for association with the data they have gathered. 5

1. Exactly one of the calculated expected frequencies for the \(\chi ^ { 2 }\)-test is less than 5
   Explain why the number of degrees of freedom for the test is 90
   5
2. The school management team claims that there is an association between the school a student attends and the activity they choose. The test statistic is 124.8 Test the claim using the \(1 \%\) level of significance.
   5
3. During the hypothesis test, the value of \(\frac { ( O - E ) ^ { 2 } } { E }\), where \(O\) is the observed frequency and \(E\) is the expected frequency, was calculated for each group of students. The values for four groups of students are shown in the table below.

   Group	\(\frac { ( O - E ) ^ { 2 } } { E }\)
   Attends school 3 and chose activity 1	0.01
   Attends school 8 and chose activity 3	18.5
   Attends school 8 and chose activity 7	24.2
   Attends school 11 and chose activity 7	49.0

   State, with a reason, which of the four groups of students represents the strongest source of association.