Assuming that all rankings are equally likely, show that \(\mathrm { P } ( R \leqslant 17 ) = \frac { 2 } { 231 }\).
The marks of 5 randomly chosen students from School \(A\) and 6 randomly chosen students from School \(B\), who took the same examination, achieving different marks, were ranked. The rankings are shown in the table.
Rank
1
2
3
4
5
6
7
8
9
10
11
School
\(A\)
\(A\)
\(A\)
\(B\)
\(A\)
\(A\)
\(B\)
\(B\)
\(B\)
\(B\)
\(B\)
For a Wilcoxon rank-sum test, obtain the exact smallest significance level for which there is evidence of a difference in performance at the two schools.