CAIE FP2 2013 June — Question 7

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionJune
TopicHypothesis test of a normal distribution

7 Each of a random sample of 6 cyclists from a cycling club is timed over two different 10 km courses. Their times, in minutes, are recorded in the following table.
Cyclist\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)
Course 118.517.819.222.316.520.0
Course 220.220.418.120.618.520.5
Assuming that differences in time over the two courses are normally distributed, test at the \(10 \%\) significance level whether the mean times over the two courses are different.