Question No: 1

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)
backethead<-c(23,23,23,21,21,22,20,22,22,22,19,19,21,18,18)
dat<-data.frame(basic,conehead,backethead)
boxplot(dat$basic,dat$conehead,dat$backethead,names=c("Basic","Conhead","Backethead"), main= "Boxplot of Zoombie")

Comments: We can see from the side by side boxplot all means are same for Zoombie but variance don’t look similier. IQR looks similar shape.

Question No: 2

Hypothesis: Ho;u1=u2=u3 , Alternative Hypothesis Ha; one of the means differs.

library(tidyr)
dat1<-pivot_longer(data=dat,c(basic,conehead,backethead))
anova_model<-aov(value~name,data=dat1)
summary(anova_model)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## name         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

Comments: from the summary we see that p value 1.79e-14, which is very smaller that 0.05, so we reject the null hypothesis Ho. so we can say that one of the mean of zoombie will differ from others.

plot(anova_model)

## hat values (leverages) are all = 0.06666667
##  and there are no factor predictors; no plot no. 5

Comments: from the normality QQ plot, it looks fairly normal. and equality of variance of each one.

library(car)
## Warning: package 'car' was built under R version 4.1.3
## Loading required package: carData
Tukey<-TukeyHSD(anova_model,conf.level = 0.95)
Tukey
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = value ~ name, data = dat1)
## 
## $name
##                     diff       lwr      upr     p adj
## basic-backethead     1.8 0.3461652 3.253835 0.0120723
## conehead-backethead  7.0 5.5461652 8.453835 0.0000000
## conehead-basic       5.2 3.7461652 6.653835 0.0000000
plot(Tukey)

Comment: from Tukkeu HSD, it has been seen that no pairs look significantly differ.