Problem

A large company claims that the median salary of its employees is $32\,500$. The salaries ($) of 15 randomly selected employees are listed below.

$18\,750 \quad 30\,500 \quad 125\,000 \quad 42\,500 \quad 25\,000$

$26\,000 \quad 52\,500 \quad 23\,000 \quad 27\,500 \quad 19\,500$

$25\,500 \quad 33\,000 \quad 30\,000 \quad 21\,500 \quad 29\,000$

(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.