CAIE FP2 2012 June — Question 7

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2012
SessionJune
TopicLinear combinations of normal random variables
TypePaired t-test

7 A random sample of 8 swimmers from a swimming club were timed over a distance of 100 metres, once in an outdoor pool and once in an indoor pool. Their times, in seconds, are given in the following table.
Swimmer\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)\(G\)\(H\)
Outdoor time66.262.460.865.468.864.365.267.2
Indoor time66.160.360.965.266.463.862.469.8
Assuming a normal distribution, test, at the \(5 \%\) significance level, whether there is a non-zero difference between mean time in the outdoor pool and mean time in the indoor pool.