The Mid-Distance Running Coach,Zdravko Popovich,for the Olympic Team of an Eastern

Essay

The mid-distance running coach,Zdravko Popovich,for the Olympic team of an eastern European country claims that his six-month training program significantly reduces the average time to complete a 1500-meter run.Five mid-distance runners were randomly selected before they were trained with coach Popovich's six-month training program and their completion time of 1500-meter run was recorded (in minutes).After six months of training under coach Popovich,the same five runners' 1500 meter run time was recorded again the results are given below.Assuming the difference in running times is normally distributed. $$\begin{array} { l c c c c } \text { Runner } & 1 & 2 & 3 & 4 \\\text { Completion time before training } & 5.9 & 7.5 & 6.1 & 6.8 \\\text { Completion time after training } & 5.4 & 7.1 & 6.2 & 6.5\end{array}$$
-Construct the appropriate 95% confidence interval for the average change in completion time.