OCR Further Statistics 2018 March — Question 4

Exam BoardOCR
ModuleFurther Statistics (Further Statistics)
Year2018
SessionMarch
TopicWilcoxon tests

4 Sheena travels to school by bus. She records the number of minutes, \(T\), that her bus is late on each of 32 days. She believes that on average \(T\) is greater than 5, and she carries out a significance test at the \(5 \%\) level.
  1. State a condition needed for a Wilcoxon test to be valid in this case. Assume now that this condition is satisfied.
  2. State an advantage of using a Wilcoxon test rather than a sign test.
  3. Calculate the critical region for the test, in terms of a variable which should be defined.