1 Question # 3:

Part 1:

Reading the data:

basic<-c(21,20,25,22,21,22,22,24,24,23,21,25,23,24,24)
conehead<-c(28,28,25,29,29,27,30,29,29,29,30,26,26,26,28)
Buckethead<-c(23,23,23,21,21,22,20,22,22,22,19,19,21,18,18)
games<-c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
games<-as.factor(games)

BoxPlot:

boxplot(basic,conehead,Buckethead, main="Box Plot of Zombie type vs No of kills", xlab="Zombie types", ylab="No of Kills")

Comments:

--> The interquartile ranges of all zombie types seems fairly equal.

--> And from the size of the boxes we can see that variances are almost equal

--> Although the mean values seem to vary

Part 2:

Hypothesis:

Null:\[H_O:\mu_{1}=\mu_{2}=\mu_{3}=\mu\]

Alternative:\[Atleast \space one \space of\space \mu_{i}\space differs\]

Z<-c(21,20,25,22,21,22,22,24,24,23,21,25,23,24,24,28,28,25,29,29,27,30,29,29,29,30,26,26,26,28,23,23,23,21,21,22,20,22,22,22,19,19,21,18,18)
Ty<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3)
Ty<-as.factor(Ty)
dat1<-data.frame(Z,Ty)
str(dat1)
## 'data.frame':    45 obs. of  2 variables:
##  $ Z : num  21 20 25 22 21 22 22 24 24 23 ...
##  $ Ty: Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
model1<-aov(Z~Ty)
summary(model1)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## Ty           2  396.4  198.20    73.8 1.79e-14 ***
## Residuals   42  112.8    2.69                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Conclusion:

---> Since the P-value is very small i.e. (1.79e-14) compared to 0.05 sig level, we reject Null Hypothesis and conclude that the means differ.

Part # 3:

plot(model1)

Comments:

---> From the residual plot we can see that residual are evenly spread or distributed over the fitted values. They make a rectangular shape denoting that variances are equal.

---> The NPP plot is somewhat unusual but we will assume constant normality.

Part# 4:

TukeyHSD(model1)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Z ~ Ty)
## 
## $Ty
##     diff       lwr        upr     p adj
## 2-1  5.2  3.746165  6.6538348 0.0000000
## 3-1 -1.8 -3.253835 -0.3461652 0.0120723
## 3-2 -7.0 -8.453835 -5.5461652 0.0000000
plot(TukeyHSD(model1))

Comment:

---> We can see from the plot that all possible pairs of mean differ significantly as no pair lies over zero interval.