t-Test(2)

T-Test Analysis based on the “Sinking of the RMS Titanic”

This is a report on the t-Test analysis on the age of the tittanic survivors and of those who died.

setwd("D:/desktop/Data Analytics internship-sameer mathur/work/datasets")
titanic.df<-read.csv(paste("Titanic Data.csv", sep=""))
View(titanic.df)

4b: table showing the average age of the survivors and the average age of the people who died

survived.mean <- aggregate(titanic.df$Age, list(titanic.df$Survived), mean)
colnames(survived.mean)[2] <- "Age"
colnames(survived.mean)[1] <- "Survived or Not"
survived.mean

##   Survived or Not      Age
## 1               0 30.41530
## 2               1 28.42382

The average age of survivors is 30 and the average age of the people who died is 28.

4c: t-Test:

H2: The Titanic survivors were younger than the passengers who died.

1. Inspecting the structure of the data

head(titanic.df)

##   Survived Pclass    Sex  Age SibSp Parch    Fare Embarked
## 1        0      3   male 22.0     1     0  7.2500        S
## 2        1      1 female 38.0     1     0 71.2833        C
## 3        1      3 female 26.0     0     0  7.9250        S
## 4        1      1 female 35.0     1     0 53.1000        S
## 5        0      3   male 35.0     0     0  8.0500        S
## 6        0      3   male 29.7     0     0  8.4583        Q

2. summary statistics

table(titanic.df$Survived)

## 
##   0   1 
## 549 340

summary(titanic.df$Age)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.40   22.00   29.70   29.65   35.00   80.00

3. Average age of survivors and people who died

survived.mean

##   Survived or Not      Age
## 1               0 30.41530
## 2               1 28.42382

4. Graphical represenation

boxplot(Age ~ Survived, data=titanic.df, yaxt="n", horizontal = TRUE, ylab="Survived or Not", xlab="Age", main="Comparison of Age of survivors and people who died", col=c("blue", "turquoise"))
axis(side=2, at=c(1,2), labels=c("Died", "Survived"))

log.transformed.Age = log(titanic.df$Age)

Hypothesis 2: The Titanic survivors were younger than the passengers who died.

NULL hypothesis: -" There is no significant difference between age of titanic survivors and those who died."

t.test(log.transformed.Age~titanic.df$Survived,var.equal = TRUE)

## 
##  Two Sample t-test
## 
## data:  log.transformed.Age by titanic.df$Survived
## t = 3.844, df = 887, p-value = 0.0001297
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.09102778 0.28094770
## sample estimates:
## mean in group 0 mean in group 1 
##        3.304318        3.118330

• Since the p-value is less than 0.05, we reject the null hypothesis that there’s no difference between the means and conclude that a significant difference does exist.In this case, it is the age of titanic survivors and those who died and that we would reject our NULL hypothesis, but we do not accept the hypothesis H2.
• Mean age of titanic survivors is 30 and the mean age of those who died is 28.
• The box plot revealed the presence of a few outliners in case of age of those who died.