When should Yates' correction be applied when carrying out a \(\chi ^ { 2 }\) test?
Two vaccines against typhoid fever, \(A\) and \(B\), were tested on a total of 700 people in Nepal during a particular year. The vaccines were allocated randomly and whether or not typhoid had developed was noted during the following year. The results are shown in the table.
\multirow{2}{*}{}
Vaccines
\cline { 2 - 3 }
\(A\)
\(B\)
Developed typhoid
19
4
Did not develop typhoid
310
367
Carry out a suitable \(\chi ^ { 2 }\) test at the \(1 \%\) significance level to determine whether the outcome depends on the vaccine used. Comment on the result.