| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | May |
| Marks | 10 |
| Topic | Wilcoxon tests |
| Type | Wilcoxon rank-sum test (Mann-Whitney U test) |
| Difficulty | Standard +0.3 This is a straightforward application of the Wilcoxon rank-sum test with clearly stated hypotheses, given rank sum, and standard significance level. Students need to calculate the test statistic, find critical values from tables, and make a conclusion. While it requires knowledge of a specific non-parametric test (slightly specialized), the execution is mechanical with no conceptual complications or novel problem-solving required. |
| Spec | 5.07d Paired vs two-sample: selection |
4. A university course was taught by two different professors. Students could choose whether to attend the lectures given by Professor $Q$ or the lectures given by Professor $R$. At the end of the course all the students took the same examination.
The examination marks of a random sample of 30 students taught by Professor $Q$ and a random sample of 24 students taught by Professor $R$ were ranked. The sum of the ranks of the students taught by Professor $Q$ was 726 .
Test at the $5 \%$ significance level whether there is a difference in the ranks of the students taught by the two professors.\\[0pt]
[10]\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q4 [10]}}