9231 P42 - Nov 2025 - Q1 - 6 marks
A large company claims that the median salary of its employees is \(\$32500\). The salaries, in dollars, of 15 randomly selected employees are listed below.
| \(18750\) | \(30500\) | \(125000\) | \(42500\) | \(25000\) | \(26000\) | \(52500\) | \(23000\) | \(27500\) | \(19500\) | \(25500\) | \(33000\) | \(30000\) | \(21500\) | \(29000\) |
(a) Explain why a Wilcoxon signed-rank test may not be appropriate to test the company's claim in this case.
(b) Carry out a sign test at the \(10\%\) significance level to investigate the company's claim.
9231 P41 - Jun 2024 - Q2 - 5 marks
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 15 students in each of the examinations are as follows.
Use a sign test, at the \(10 \%\) significance level, to test whether, on average, the practical examination marks are higher than the written examination marks.