The morley data in the base R contains the classical data of Michaelson and Morley on the speed of light, recording five experiments of $20$ consecutive runs each. The response is the speed of light measurement Speed. The experiment is Expt and the run is Run. See the documentation $?$morley. Use the str function to check that there are $100$ observations of the variables Speed, Expt and Run; all integer variables.

$($a$)$ Find the grand mean of Speed.

$($b$)$ Convert the variables Expt and Run to factors.

$($c$)$ Display a boxplot of Speed by Expt.

$($d$)$ Test the null hypothesis that means of Speed are equal among five experiments $($Expt$)$ at the level

$\backslash$alpha $=0\mathrm{.}05.$

$($e$)$ If the null hypothesis is rejected, analyze in which pair$($s$)$ among the five experiments are there significant

difference of Speed.The morley data in the base R contains the classical data of Michaelson and Morley on the speed of light, recording five experiments of $20$ consecutive runs each. The response is the speed of light measurement Speed. The experiment is Expt and the run is Run. See the documentation $?$morley. Use the str function to check that there are $100$ observations of the variables Speed, Expt and Run; all integer variables.

$($a$)$ Find the grand mean of Speed.

$($b$)$ Convert the variables Expt and Run to factors.

$($c$)$ Display a boxplot of Speed by Expt.

$($d$)$ Test the null hypothesis that means of Speed are equal among five experiments $($Expt$)$ at the level

$\backslash$alpha $=0\mathrm{.}05.$

$($e$)$ If the null hypothesis is rejected, analyze in which pair$($s$)$ among the five experiments are there significant

difference of Speed.