9231 P43 - Jun 2020 - Q6 - 11 marks
6826
A biologist is studying the effect of nutrients on the heights to which plants grow. A random sample of 24 similar young plants is divided into two equal groups \(A\) and \(B\). The plants in group \(A\) are fed with nutrients and water and the plants in group \(B\) are given only water. After four weeks, the height, in cm, of each plant is measured and the results are as follows.
| Group \(A\) | 12.3 | 11.8 | 12.1 | 13.2 | 11.1 | 10.6 | 13.8 | 12.0 | 12.2 | 12.4 | 13.5 | 13.9 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Group \(B\) | 11.7 | 10.8 | 10.9 | 11.3 | 11.2 | 12.6 | 11.0 | 10.5 | 11.9 | 12.5 | 10.7 | 11.6 |
The biologist decides to carry out a test at the \(5\%\) significance level to test whether the nutrients have resulted in an increase in growth.
(a) She carries out a Wilcoxon rank-sum test. Give a reason why this is an appropriate choice of test.
(b) Carry out the Wilcoxon rank-sum test for these results.
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