Non-parametric tests — AS & A Level Further Mathematics (9231) questions by topic
Rank-based hypothesis testing runs through this topic: comparing paired throw distances before and after hot weather, testing agreement between two teachers' logo marks, and testing whether a sample of metal-disc diameters is consistent with a claimed median.
Carry out, test, show, state and explain lead the command words across 18 questions from 2023 to 2025 papers, worth from 5 to 16 marks, where hypotheses must reference the population median rather than the mean. Working through each Wilcoxon or sign-test calculation with instant marking flags a wrong critical value or a hypothesis wording slip immediately, rather than after the conclusion has already been drawn incorrectly.
What examiners look for
- A recurring criticism is using mu, the mean, instead of m, the median, or referring to the median of the sample data rather than the population median in the hypotheses.
- Examiners note a common numerical slip: computing 55 correctly but then using 8(8 + 9 + 1) - 55 = 89 as the test statistic.
- A common mistake was using the incorrect critical value 17 instead of 21.
- Reports flag explaining a result in words only, without the required numerical justification, as insufficient for credit.
- Strong answers referred to the fact that outliers affect a t-test more than a Wilcoxon rank-sum test, and noted that a test statistic of 20, being below the critical value of 21, changes the test's conclusion.
May–June 2025, Paper 41
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…
Answer this question and get it marked →May–June 2025, Paper 42
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…
Answer this question and get it marked →May–June 2025, Paper 43
A researcher claims that older people take longer to react to a sudden loud noise than younger people. To investigate this, the researcher randomly selects 6 people over 50 years…
Answer this question and get it marked →May–June 2025, Paper 44
The level of sound produced by a particular type of machine was measured for a random sample of 11 such machines. The results, in suitable units, are shown below. Machine A B C D…
Answer this question and get it marked →May–June 2024, Paper 41
A large number of students are taking a Physics course. They are assessed by a practical examination and a written examination. The marks out of 100 obtained by a random sample of…
Answer this question and get it marked →A factory produces metal discs. The manager claims that the diameters of these discs have a median of 22.0 mm. The diameters, in mm, of a random sample of 12 discs produced by…
Answer this question and get it marked →May–June 2024, Paper 42
A large number of students are taking a Physics course. They are assessed by a practical examination and a written examination. The marks out of 100 obtained by a random sample of…
Answer this question and get it marked →A factory produces metal discs. The manager claims that the diameters of these discs have a median of 22.0 mm. The diameters, in mm, of a random sample of 12 discs produced by…
Answer this question and get it marked →May–June 2024, Paper 43
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…
Answer this question and get it marked →October–November 2024, Paper 41
A school with a large number of students is updating its logo. Each student has designed a new logo and two teachers have each awarded a mark out of 50 for each logo. The marks…
Answer this question and get it marked →October–November 2024, Paper 42
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. After a month of intensive…
Answer this question and get it marked →October–November 2024, Paper 43
A school with a large number of students is updating its logo. Each student has designed a new logo and two teachers have each awarded a mark out of 50 for each logo. The marks…
Answer this question and get it marked →May–June 2023, Paper 41
A random sample of 13 technology companies is chosen and the numbers of employees in 2018 and in 2022 are recorded. Company A B C D E F G H I J K L M --- --- --- --- --- --- ---…
Answer this question and get it marked →May–June 2023, Paper 42
A random sample of 13 technology companies is chosen and the numbers of employees in 2018 and in 2022 are recorded. Company A B C D E F G H I J K L M Number in 2018 104 19 126 234…
Answer this question and get it marked →May–June 2023, Paper 43
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…
Answer this question and get it marked →October–November 2023, Paper 41
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…
Answer this question and get it marked →October–November 2023, Paper 42
A company is deciding which of two machines, X and Y, can make a certain type of electrical component more quickly. The times taken, in minutes, to make one component of this type…
Answer this question and get it marked →October–November 2023, Paper 43
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…
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