Problem

A school is conducting an experiment to see whether the distance that children can throw a ball increases in hot weather. On a cold day, all the children at the school were asked to throw a ball as far as possible. The distances thrown were measured and recorded. The median distance thrown by a random sample of 25 of the children was $22.0$ m. The children were asked to throw the ball again on a hot day. The distances thrown by the same 25 children were measured and recorded and these distances, in m, are shown below.

$$\begin{gathered} 21.2 \qquad 23.5 \qquad 22.9 \qquad 18.6 \qquad 19.4 \\ 22.1 \qquad 26.5 \qquad 20.2 \qquad 25.7 \qquad 20.6 \\ 22.3 \qquad 17.4 \qquad 22.2 \qquad 27.0 \qquad 23.9 \\ 28.2 \qquad 22.6 \qquad 27.2 \qquad 23.0 \qquad 23.7 \\ 19.8 \qquad 22.7 \qquad 23.3 \qquad 21.5 \qquad 24.3 \end{gathered}$$

The teacher claims that on average the distances thrown will be further when it is hot.

Carry out a Wilcoxon signed-rank test, at the 5% significance level, to test whether the data supports the teacher’s claim.