1 Gerry runs 5000 -metre races for his local athletics club. His coach has been monitoring his practice times for several months and he believes that they can be modelled using a Normal distribution with mean 15.3 minutes. The coach suggests that Gerry should try running with a pacemaker in order to see if this can improve his times. Subsequently a random sample of 10 of Gerry's times with the pacemaker is collected to see if any reduction has been achieved. The sample of times (in minutes) is as follows.
$$\begin{array} { l l l l l l l l l l }
14.86 & 15.00 & 15.62 & 14.44 & 15.27 & 15.64 & 14.58 & 14.30 & 15.08 & 15.08
\end{array}$$
- Why might a \(t\) test be used for these data?
- Using a \(5 \%\) significance level, carry out the test to see whether, on average, Gerry's times have been reduced.
- What is meant by 'a \(5 \%\) significance level'? What would be the consequence of decreasing the significance level?
- Find a \(95 \%\) confidence interval for the true mean of Gerry's times using a pacemaker.