5 A one-tail sign test of a population median is to be carried out at the \(5 \%\) significance level using a sample of size \(n\).
- Show by calculation that the test can never result in rejection of the null hypothesis when \(n = 4\).
The coach of a college swimming team expects Elena, the best 50 m freestyle swimmer, to have a median time less than 30 seconds. Elena found from records of her previous 72 swims that 44 were less than 30 seconds and 28 were greater than 30 seconds.
- Stating a necessary assumption, test at the \(5 \%\) significance level whether Elena's median time for the 50 m freestyle is less than 30 seconds.