Read the titanic dataset

titanic <- read.csv(paste("Titanic Data.csv", sep=""))
head(titanic)  # first few rows of the data frame
##   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

view data to confirm it is exactly matching the one we saw in the excel file

View(titanic)

3a Use R to count the total number of passengers on board the Titanic.

totalpassenger<-table(titanic$Sex)
totalpassenger
## 
## female   male 
##    312    577
addmargins(totalpassenger)
## 
## female   male    Sum 
##    312    577    889

second method

dim(titanic)[1]
## [1] 889

here total number of passengers on board were 889

3b Use R to count the number of passengers who survived the sinking of the Titanic.

survivedtable<-table(titanic$Survived)
survivedtable[2]
##   1 
## 340

second method

nrow(subset(titanic, Survived == 1))
## [1] 340
#or use the length function
length(titanic$Survived[titanic$Survived=="1"])
## [1] 340

so the number of passengers who survived the sinking titanic was 340

3c-Use R to measure the percentage of passengers who survived the sinking of the Titanic.

prop.table(survivedtable)
## 
##         0         1 
## 0.6175478 0.3824522
(100*prop.table(survivedtable))[2]
##        1 
## 38.24522

second method

x<-dim(titanic)[1]
y<-survivedtable[2]
z<-y/x
100*z
##        1 
## 38.24522

so the percentage of passengers surviving the sinking titanic is 38.245%

3d Use R to count the number of first-class passengers who survived the sinking of the Titanic.

psurvived<-xtabs(~Survived+Pclass,data = titanic)
addmargins(psurvived)
##         Pclass
## Survived   1   2   3 Sum
##      0    80  97 372 549
##      1   134  87 119 340
##      Sum 214 184 491 889
addmargins(psurvived)[2,1]
## [1] 134

so the no. of first class passengerswho survived the sinking of the Titanic.= 134

3e Use R to measure the percentage of first-class passengers who survived the sinking of the Titanic.

prop.table(psurvived)
##         Pclass
## Survived          1          2          3
##        0 0.08998875 0.10911136 0.41844769
##        1 0.15073116 0.09786277 0.13385827
(100*prop.table(psurvived))[2,1]
## [1] 15.07312

so the percentage of first-class passengers who survived the sinking of the Titanic= 15.073%

3f Use R to count the number of females from First-Class who survived the sinking of the Titanic.

femalesurvivor<-xtabs(~Survived+Sex+Pclass,data = titanic)
femalesurvivor
## , , Pclass = 1
## 
##         Sex
## Survived female male
##        0      3   77
##        1     89   45
## 
## , , Pclass = 2
## 
##         Sex
## Survived female male
##        0      6   91
##        1     70   17
## 
## , , Pclass = 3
## 
##         Sex
## Survived female male
##        0     72  300
##        1     72   47
ftable(femalesurvivor)
##                 Pclass   1   2   3
## Survived Sex                      
## 0        female          3   6  72
##          male           77  91 300
## 1        female         89  70  72
##          male           45  17  47
ftable(femalesurvivor)[3,1]
## [1] 89

so the number of females from First-Class who survived the sinking of the Titanic=89 note- we have used ftable function to give a compact view of our table.

3g Use R to measure the percentage of survivors who were female first class

prop.table(ftable(femalesurvivor))
##                 Pclass           1           2           3
## Survived Sex                                              
## 0        female        0.003374578 0.006749156 0.080989876
##          male          0.086614173 0.102362205 0.337457818
## 1        female        0.100112486 0.078740157 0.080989876
##          male          0.050618673 0.019122610 0.052868391
(100*prop.table(ftable(femalesurvivor)))
##                 Pclass          1          2          3
## Survived Sex                                           
## 0        female         0.3374578  0.6749156  8.0989876
##          male           8.6614173 10.2362205 33.7457818
## 1        female        10.0112486  7.8740157  8.0989876
##          male           5.0618673  1.9122610  5.2868391
(100*prop.table(ftable(femalesurvivor)))[3,1]
## [1] 10.01125

so percentage of female survivor firt class= 10.01125%

3h Use R to measure the percentage of females on board the Titanic who survived

femsurv<-xtabs(~Survived+Sex,data = titanic)
prop.table(femsurv)
##         Sex
## Survived     female       male
##        0 0.09111361 0.52643420
##        1 0.25984252 0.12260967
(100*prop.table(femsurv))
##         Sex
## Survived    female      male
##        0  9.111361 52.643420
##        1 25.984252 12.260967
(100*prop.table(femsurv))[2,1]
## [1] 25.98425

so percentage of female survived on board the sinking titanic=25.98425%

3i Run a Pearson’s Chi-squared test to test the following hypothesis: Hypothesis: The proportion of females onboard who survived the sinking of the Titanic was higher than the proportion of males onboard who survived the sinking of the Titanic

chisq.test(femsurv)
## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  femsurv
## X-squared = 258.43, df = 1, p-value < 2.2e-16
chisq.test(femsurv)$p.value
## [1] 3.77991e-58

here we can see that p value is less than 0.05.

so we reject the null hypothes we say that in the wake of given titanic data we are accepting the alternative hypothesis that The proportion of females onboard who survived the sinking of the Titanic was not higher than the proportion of males onboard who survived the sinking of the Titanic

important note-rejecting null does not prove null hypothesisi to be false.it says in the wake of given data null hypothesis does not seem to be plausible hypothesis.