CAIE FP2 2008 November — Question 7

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2008
SessionNovember
TopicHypothesis test of a normal distribution

7 The pulse rate of each member of a random sample of 25 adult UK males who exercise for a given period each week is measured in beats per minute. A \(98 \%\) confidence interval for the mean pulse rate, \(\mu\) beats per minute, for all such UK males was calculated as \(61.21 < \mu < 64.39\), based on a \(t\)-distribution.
  1. Calculate the sample mean pulse rate and the standard deviation used in the calculation.
  2. State an assumption necessary for the validity of the confidence interval.
  3. The mean pulse rate for all UK males is 72 beats per minute. State, giving a reason, if it can be concluded that, on average, UK males who exercise have a reduced pulse rate.