A serious drought related problem for farmers is the spread of aflatoxin, a highly toxic substance caused by mold, which contaminates field com. In higher levels of contamination, aflatoxin is potentially hazardous to animal and possibly human health. Two sprays, A and B$,$ have been deyeloped to control aflatoxin in field com. The sprays are then $($randomly assigned$)$ to two plots of contaminated com fields and $8$ ears of com were randomly selected within each field. The amount of aflatoxin, in parts per billion, present in the com after spraying was recorded.

indepadat

$\backslash$table$[[$Com$,$Spray A$,$Spray B$,$Total$],[1,29,23,52],[2,26,30,56],[3,26,19,45],[4,4,19,23],[5,28,10,38],[6,29,12,41],[7,27,32,59],[8,3,10,13],[$Total$,172,155,327]]$

${\displaystyle \underset{i}{\overset{?}{}}}{\displaystyle \underset{j}{\overset{?}{}}}{Y}_{ij}^2=8,091?$

$($i$)$ State the appropriate assumptions.

$($ii$)$ Test for equal variances if it is needed at $=0\mathrm{.}10.$

$($iii$)$ Perform a statistical analysis and construct an appropriate confidence interval. Use $=0\mathrm{.}10.$

$($b$)$ Many industrial air pollutants adversely affect plants. Sulphur dioxide causes leaf damage in the form of intraveinal bleaching in many sensitive plants. In the study of the effect of a given concentration of sulphur dioxide in the air on three two types of garden vegetables, $40$ plants of each type are exposed to the pollutant under controlled greenhouse conditions. The numper of severe leaf damage is recorded.

$\backslash$table$[[,$Slight,Leaf Damage,$],[$Spinach$,3,12,25,40],[$Tomato$,4,21,15,40],[$Total$,7,33,40,80]]$

${\displaystyle \underset{?}{\overset{?}{}}}{\displaystyle \underset{?}{\overset{?}{}}}{Y}_4^2=1,460$

Perform an appropriste staristical analysis. Test at the $0\mathrm{.}10$ level of significance.

$[25$ mark$]$