10 Three new flu vaccines, \(A , B\) and \(C\), were tested on 500 volunteers. The vaccines were assigned randomly to the volunteers and 178 received \(A , 149\) received \(B\) and 173 received \(C\). During the following year, 30 of the volunteers given \(A\) caught flu, 29 of the volunteers given \(B\) caught flu, and 16 of the volunteers given \(C\) caught flu. Carry out a suitable test for independence at the 5\% significance level. Without using a statistical test, decide which of the vaccines appears to be most effective.