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 $($kg$/$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 Excel spreadsheet, $$PtA animal$$

Question $1$

$1.$ 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$)(15)$

Question $2$

$2.$ 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$).(15)$

Question $3$

$3.$ 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$).(20)\backslash$table$[[,,$B$,$C$,$D$,E,F,$G$,H$