6 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.
| 21.2 | 23.5 | 22.9 | 18.6 | 19.4 |
| 22.1 | 26.5 | 20.2 | 25.7 | 20.6 |
| 22.3 | 17.4 | 22.2 | 27.0 | 23.9 |
| 28.2 | 22.6 | 27.2 | 23.0 | 23.7 |
| 19.8 | 22.7 | 23.3 | 21.5 | 24.3 |
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.
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