PART A

You are a scientist interested in analysing milk production performance in dairy cattle. You used $10$ cows from $3$ breeds $($Friesian$,$ Ayrshire and Shorthorn$)$ and recorded: parity $($number of times the cow calved$),$ milk yield $(k\frac{g}{?}$ day$)$ for the current lactation, milk yield $($kg$/$day$)$ for the previous lactation, milk butterfat for the current lactation $(\%),$ history of mastitis $($udder infection$)$ and history of metritis $($uterine infection$).$ Raw data are given in the table $1$ below.

Question $1$

You want to assess the association between "history of mastitis" and "history of metritis".

a$.$ Which test should you use? Justify your answer

b$.$ Carry out the analysis and a short report of your statistical method and results $($as would appear in a scientific journal article$/$dissertation$)$

Question $2$

You want to test if there is a difference in parity between Friesian, Ayrshire and Shorthorn

a$.$ Which test should you use? Justify your answer

b$.$ Carry out the test and produce a short report of your statistical method and results $($as would appear in a scientific journal article$/$dissertation$).$

Question $3$

Do the breeds and the production systems affect the means of "milk yield $($kg$/$day$)$ for actual lactation". Is there an interaction?

a$.$ Which test should you use? Justify your answer

b$.$ Write a short method and results $($including graph if appropriate$)$ for your statistical test $($as it would appear in a journal article$/$dissertation$).$

Table $1$ PtAanimal

$\backslash$table$[[$Breed$,\backslash$table$[[$Syste$],[m$