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CAIE A-Level Further Math 4.4.2 The basis of the sign test

Practise the assumptions behind sign, Wilcoxon signed-rank and rank-sum tests, and how those assumptions affect test choice.

Syllabus
2028–2030
Course
Further Mathematics 9231
Level
AS

Exam points

  • state symmetry or similar-shape assumptions needed for Wilcoxon tests to be valid
  • compare a sign test with a Wilcoxon test using the magnitudes of differences
  • explain why skewness or outliers can make a Wilcoxon signed-rank test unsuitable

4.4.2—The basis of the sign test question 1

[Maximum number: 1]

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. The marks are shown in the table.

Table for Question 4.4.2—The basis of the sign test question 1 — CAIE A-Level Further Math AS

State an assumption that you have made in carrying out the test in part (a).

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