dat<-read.csv(“https://raw.githubusercontent.com/tmatis12/datafiles/main/US_Japanese_Cars.csv”)na.string= dat1<-dat\(ï..USCars dat2<-dat\)JapaneseCars library(dplyr) ##### Answer to Question 1 # To be considered large enough , sample count has to be more than 40 # the count of japanese vars is: there are both lesss than 40 and therefore not large enough to # assume the central limit theorem count(dat1) count(dat2) ?count
qqnorm(dat1, main=“mpg of uscar”) qqline(dat1) qqnorm(dat2, main=“mpg of japanesecar”) qqline(dat2) # both uscars and japanese cars follows a normal distribrution because all data point falls on the normal regression line ##### Question 3 # comparing variance of uscars and japanesecars boxplot(dat1,dat2, names=c(“uscars”,“japanesecars”),main=“BoxPlot of MPg”) # the boxplot suggest too big of difference between the var of us cars and japanese cars ##### Question 4 # data transformation loguscar<-log(dat1) logjapancar<-log(dat2) #### checking normality of transformed data qqnorm(loguscar, main=“mpg uscar transformed data”) qqline(loguscar) qqnorm(logjapancar,main=“mpg japanesecar transformed data”) qqline(logjapancar) # both plot follow the normal regression line , therefore are normally distributed ##### comparing variance of transformed data boxplot(loguscar,logjapancar, names=c(“uscars”,“japanesecars”),main=“Boxplot of transformed MPg data”) # Yes the varriance are constant ##### Setting the hypothesis # Ho: Mean1-Mean2=0 # Ha: Mean1 =/= Mean 2, ,Note" =/= " means not equal" ##### T-test t.test(loguscar,logjapancar,var.equal = TRUE, alternative = “less”) ### conclusion ### the p-value = 6.528e-14 , very low compared to the significance level ### therefore we fail to reject null hypothesis