Problem

A sports college keeps records of the times taken by students to run one lap of a running track. The population median time taken is 51.0 seconds. After a month of intensive training, a random sample of 22 new students run one lap of the track, giving times, in seconds, as follows.

$$\begin{gathered} 51.3 \qquad 52.0 \qquad 53.4 \qquad 49.2 \\ 49.3 \qquad 51.1 \qquad 52.2 \qquad 47.2 \\ 53.0 \qquad 48.5 \qquad 49.4 \qquad 50.3 \\ 50.8 \qquad 51.6 \qquad 49.1 \qquad 52.3 \\ 51.8 \qquad 52.4 \qquad 47.9 \qquad 48.9 \\ 50.6 \qquad 51.9 \end{gathered}$$

It is claimed that the intensive training has led to a decrease in the median time taken to run one lap of the track.

Carry out a Wilcoxon signed-rank test, at the 5% significance level, to test whether there is sufficient evidence to support the claim.