$1)$ In this lab, we will study the relationship between Year of program, and amount of

Sleep, using the data in stat$2$p$98$survey.csv$$ on Brightspace. The response variable

for this analysis will be the $$how many hours did you sleep last night$$ question on

the survey, and the factor of interest is $$year of program$,$ with five levels: $1$st$,2$nd$,$

$3$rd$,4$th$,$ or $5+.$

In your lab report, you should:

a$)[2]$ Write a brief introduction to the problem $(1-2$ sentences$)$ and then wri te

down the probability model for this analysis $-$ describe any variables, parameters,

and assumptions.

b$)[2]$ Rename the relevant columns of the data frame to be $$Year$$ and $$Sleep$$

respectively. Rename the levels of the $$Year$$ factor to be easier to read, for

example

mydata$Year$[$mydata$Year $==1$st $(<5$ credits complete$)]=1$st$$

c$)[2]$ Use the aov$()$ function in R to test the hypothesis H$0$ : $\backslash$tau i $=\backslash$tau j

for all i$,$ j

against the alternative Ha : $\backslash$tau i $=\backslash$tau j

for at least one i$,$ j at the $\backslash$alpha $=0\mathrm{.}05$ level.

Include the R output in your report.