Data Preparation

file_path <- "/Users/kehindeoladele/Downloads/US_Japanese_Cars.csv"

DF <- read.csv(file_path, fileEncoding = "UTF-8-BOM")

US <- na.omit(DF$USCars)
Japan <- na.omit(DF$JapaneseCars)

length(US)
## [1] 35
length(Japan)
## [1] 28
summary(US)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    9.00   14.00   15.00   15.97   18.00   28.00
summary(Japan)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   18.00   24.00   27.00   26.75   31.00   35.00

The samples contain 35 U.S. cars and 28 Japanese cars.

1. Original Normal Probability Plots

par(mfrow = c(1, 2))

qqnorm(US, main = "NPP: U.S. Cars", col = "steelblue", pch = 19)
qqline(US, col = "red", lwd = 2)

qqnorm(Japan, main = "NPP: Japanese Cars", col = "hotpink", pch = 19)
qqline(Japan, col = "red", lwd = 2)

par(mfrow = c(1, 1))

The U.S. data depart from the line in the upper tail, indicating right skewness. The Japanese observations are closer to a straight line and appear approximately Normal.

2. Original Side-by-Side Boxplots

boxplot(
  US, Japan,
  names = c("U.S.", "Japan"),
  main = "MPG by Country",
  ylab = "MPG",
  col = c("steelblue", "hotpink")
)

IQR(US)
## [1] 4
IQR(Japan)
## [1] 7

The IQR for U.S. cars is noticeably larger than the IQR for Japanese cars, suggesting the equal-variance assumption is questionable on the original scale.

3. Log Transformation

logUS <- log(US)
logJapan <- log(Japan)

Transformed Normal Probability Plots

par(mfrow = c(1, 2))

qqnorm(logUS, main = "NPP: U.S. Log(MPG)", col = "steelblue", pch = 19)
qqline(logUS, col = "red", lwd = 2)

qqnorm(logJapan, main = "NPP: Japan Log(MPG)", col = "hotpink", pch = 19)
qqline(logJapan, col = "red", lwd = 2)

par(mfrow = c(1, 1))

The log transformation pulls both sets of points closer to the reference line. The U.S. points now track the line much better in the upper tail, and the Japanese points remain approximately Normal.

Transformed Side-by-Side Boxplots

boxplot(
  logUS, logJapan,
  names = c("U.S.", "Japan"),
  main = "Log(MPG) by Country",
  ylab = "Log(MPG)",
  col = c("steelblue", "hotpink")
)

IQR(logUS)
## [1] 0.2513144
IQR(logJapan)
## [1] 0.2559334

4. Hypothesis Test

mean_logUS <- mean(logUS)
mean_logJapan <- mean(logJapan)

mean_logUS
## [1] 2.741001
mean_logJapan
## [1] 3.270957
test_result <- t.test(
  logUS,
  logJapan,
  alternative = "less",
  var.equal = TRUE
)

test_result
## 
##  Two Sample t-test
## 
## data:  logUS and logJapan
## 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

Because the p-value is less than 0.05, I reject Ho. There is sufficient evidence that the population mean log(MPG) of U.S. cars is lower than that of Japanese cars.