The children at two large schools, \(P\) and \(Q\), are all given the same puzzle to solve. A random sample of size 10 is taken from the children at school \(P\). Their individual times to complete the puzzle give a sample mean of 9.12 minutes and an unbiased variance estimate of 2.16 minutes \({ }^{2}\). A random sample of size 12 is taken from the children at school \(Q\). Their individual times, \(x\) minutes, to complete the puzzle are summarised by
\(\sum x=99.6 \quad \sum(x-\bar{x})^{2}=21.5\)
where \(\bar{x}\) is the sample mean. Times to complete the puzzle are assumed to be normally distributed with the same population variance.

Test at the \(5 \%\) significance level whether the population mean time taken to complete the puzzle by children at school \(P\) is greater than the population mean time taken to complete the puzzle by children at school \(Q\).