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)
dat<-data.frame(Basic,Conehead,Buckethead)
data<-c(Basic,Conehead,Buckethead)
x<-c(rep(1,15),rep(2,15),rep(3,15))
x<-as.factor(x)

#Question 1

boxplot(Basic,Conehead,Buckethead)

#from the box plot the variance is not constant

library(tidyr)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
model<-aov(data~x)
summary(model)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## x            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

#from the annova test we get p value less than the level of signifance we reject null hypothesis

plot(model)

#By doing annova all the plots are normall

library(car)
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode
TukeyHSD(model)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = data ~ x)
## 
## $x
##     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

#there is signicificant difference between 2 and 1 pair