Data Read and Load

dat <- read.csv('https://raw.githubusercontent.com/tmatis12/datafiles/main/US_Japanese_Cars.csv')
dat
##    USCars JapaneseCars
## 1      18           24
## 2      15           27
## 3      18           27
## 4      16           25
## 5      17           31
## 6      15           35
## 7      14           24
## 8      14           19
## 9      14           28
## 10     15           23
## 11     15           27
## 12     14           20
## 13     15           22
## 14     14           18
## 15     22           20
## 16     18           31
## 17     21           32
## 18     21           31
## 19     10           32
## 20     10           24
## 21     11           26
## 22      9           29
## 23     28           24
## 24     25           24
## 25     19           33
## 26     16           33
## 27     17           32
## 28     19           28
## 29     18           NA
## 30     14           NA
## 31     14           NA
## 32     14           NA
## 33     14           NA
## 34     12           NA
## 35     13           NA

US Car and Japanese Cars Data

uscar <- dat[,1]
uscar
##  [1] 18 15 18 16 17 15 14 14 14 15 15 14 15 14 22 18 21 21 10 10 11  9 28 25 19
## [26] 16 17 19 18 14 14 14 14 12 13
jpcar <- dat[1:28,2]
jpcar
##  [1] 24 27 27 25 31 35 24 19 28 23 27 20 22 18 20 31 32 31 32 24 26 29 24 24 33
## [26] 33 32 28

Check Data Distribution

##US CARS Distribution Plot

qqnorm(uscar, main = 'US Car Q_Q Plot', col ='blue')

Japanese Car Distribution Plot

qqnorm(jpcar, main = 'Japanes Car Q_Q Plot', col= 'red' )

#2 Check Variance

boxplot(uscar, jpcar, main='Box Plot For US Car and Japanese Car', col=c('blue','red'))

comment: The plot clearly shows that the vraiance appear is not constant

#3 Apply Log Transformations

lus <- log(uscar)
ljp <- log(jpcar)

After Log conversion fo US car QQ Normal Plot

qqnorm(lus, main = 'Log US Car Q_Q Plot', col='blue')

Comment: tend lay about straight line normality ## After Log conversion fo Japanese car QQ Normal Plot

qqnorm(ljp, main = 'Log Japanease Car Q_Q Plot', col='red')

Comment: tend lay about straight line normality

#Box Plot after Log conversion of US Car and Japanese Car

boxplot(lus, ljp, main='Log Coversion Box Plot For US Car and Japanese Car', names =c("US Car", "Japanese Car"), col=c('blue', 'red'))

comment: variance is most closer after the log transformation #4. Hypothesis Test - \(H_0:\mu_{\text{UScars}} = \mu_{\test{JPCars}}\) - \(H_a:\mu_{\text{UScars}} < \mu_{\test{JPCars}}\)

#Apply Two Sample T- Test

t.test(x= lus, y = ljp,
       alternative = c("less"),
       mu = 0, paired = FALSE, var.equal = TRUE)
## 
##  Two Sample t-test
## 
## data:  lus and ljp
## t = -9.4828, df = 61, p-value = 6.528e-14
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##        -Inf -0.4366143
## sample estimates:
## mean of x mean of y 
##  2.741001  3.270957

About the P value is is than 0, we can reject the Null Hypothesis, The Sample mean of US Cars is 2.74 and Japanease Car 3.27

#Conclusions:

US car has less MPG than Japanease Car Following the normal distribution, befor log transformation variance of the sample are different, Some outliars observe in US car samples

#Load Data
dat <- read.csv('https://raw.githubusercontent.com/tmatis12/datafiles/main/US_Japanese_Cars.csv')
dat

#Observing Datas US and Japanese Car

uscar <- dat[,1]
uscar
jpcar <- dat[1:28,2]
jpcar

#Check Normal Distribution of US and Japanese Car
qqnorm(uscar, main = 'US Car Q_Q Plot', col ='blue')
qqnorm(jpcar, main = 'Japanes Car Q_Q Plot', col= 'red' )


#Check Variances using Box Plot
boxplot(uscar, jpcar, main='Box Plot For US Car and Japanese Car', col=c('blue','red'))

#Apply Log Transformations

lus <- log(uscar)
ljp <- log(jpcar)

#Check Normal Distribution After Log Conversion
qqnorm(lus, main = 'Log US Car Q_Q Plot', col='blue')
qqnorm(ljp, main = 'Log Japanease Car Q_Q Plot', col='red')

#check variance after log transformation
boxplot(lus, ljp, main='Log Coversion Box Plot For US Car and Japanese Car', names =c("US Car", "Japanese Car"), col=c('blue', 'red'))

#Apply Two Sample T-tes

t.test(x= lus, y = ljp,
       alternative = c("less"),
       mu = 0, paired = FALSE, var.equal = TRUE)