Non-parametric tests: past paper questions

Where the questions come from

• Question 1May/June 2026, paper 41Structured7 marks

  The manager of a village store is interested in the shopping habits of his customers. From previous records, the median number of items bought per customer was found to be 8. The manager believes the median number of items bought per customer has increased.

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• Question 4Oct/Nov 2025, paper 41Structured5 marks

  A researcher believes that the median $m$ of a population has changed from its known previous value $m_0$. The researcher collects a random sample of size 28. She ranks the data and calculates a test statistic $T$ using the Wilcoxon signed-rank test.

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• Question 6Oct/Nov 2023, paper 41Structured10 marks

  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.

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• Question 6Oct/Nov 2025, paper 41Structured9 marks

  Nine athletes in a club have a new coach. The coach adopts a new training programme which he believes will reduce the race times of these athletes. Each athlete completes a 1500 m time trial before and after completing the new training programme.

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• Question 6Oct/Nov 2024, paper 42Structured9 marks

  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.

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• Question 5Oct/Nov 2023, paper 42Structured16 marks

  A company is deciding which of two machines, $X$ and $Y$, can make a certain type of electrical component more quickly.

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• Question 1Oct/Nov 2025, paper 42Structured6 marks

  A large company claims that the median salary of its employees is $32500.Thesalaries($) of 15 randomly selected employees are listed below.

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• Question 3May/June 2024, paper 41Structured8 marks

  A factory produces metal discs. The manager claims that the diameters of these discs have a median of $22.0\text{ mm}$. The diameters, in mm, of a random sample of 12 discs produced by this factory are as follows.

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• Question 5May/June 2025, paper 41Structured10 marks

  Two jigsaw puzzles have the same number of pieces with identical shapes but have different pictures printed on them. One puzzle has a seaside picture and the other has a cartoon picture.

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• Question 3May/June 2023, paper 43Structured8 marks

  A large number of students took two test papers in mathematics. The teacher believes that the marks obtained in Paper 1 will be higher than the marks obtained in Paper 2. She chooses a random sample of 9 students and compares their marks.

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• Question 4May/June 2025, paper 43Structured8 marks

  A researcher claims that older people take longer to react to a sudden loud noise than younger people.

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• Question 1May/June 2024, paper 43Structured7 marks

  A college uses two assessments, $X$ and $Y$, when interviewing applicants for research posts at the college. These assessments have been used for a large number of applicants this year. The scores for a random sample of 9 applicants who took assessment $X$ are as follows.

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