The football coach randomly selected ten players and timed how long each player took to perform a certain drill. the times (in minutes) were:

Given that the football coach randomly selected ten players and timed how long each player took to perform a certain drill.

The times (in minutes) were: 7.2 10.5 9.9 8.2 11.0 7.3 6.7 11.0 10.8 12.4

The mean and tha standard deviation are obtained from the following table:

[tex]\begin{tabular} {|c|c|c|} x&$x-\bar{x}$&$(x-\bar{x})^2$\\[1ex] 7.2&-2.3&5.29\\10.5&1&1\\9.9&0.4&0.16\\8.2&-1.3&1.69\\11.0&1.5&2.25\\7.3&-2.2&4.84\\6.7&-2.8&7.84\\11.0&1.5&2.25\\10.8&1.3&1.69\\12.4&2.9&8.41\\[1ex] \Sigma x=95&&$\Sigma(x-\bar{x})^2=35.42$ \end{tabular}\\ \\ \bar{x}=\frac{\Sigma x}{n}=\frac{95}{10}=9.5\\ \\ s= \sqrt{\frac{\Sigma(x-\bar{x})^2}{n-1}} = \sqrt{\frac{35.42}{9} }=\sqrt{3.94}=1.98[/tex]

The 95% confidence interval for the mean time for all players is given by

[tex]95\% \ C.I.=\bar{x}\pm t_{(\alpha/2,\ k)}\left( \frac{s}{\sqrt{n}} \right) \\ \\ =9.5\pm t_{(0.025,\ 9)}\left( \frac{1.98}{\sqrt{10}} \right)=9.5\pm2.26016(0.626) \\ \\ =9.5\pm1.415=(8.09,\ 10.92)[/tex]