W2D1

dean.df<- read.csv("Data - Deans Dilemma.csv",sep = ",")
View(dean.df)

placedmale.df<- dean.df[ which(dean.df$Gender.B=='0') , ] 
View(placedmale.df)

placedfemale.df<- dean.df[ which(dean.df$Gender.B=='1') , ] 
View(placedfemale.df)

x=mean(placedfemale.df$Salary)
y=mean(placedmale.df$Salary)
table(x,y)

##                   y
## x                  231484.848484848
##   193288.188976378                1

H0: The average salary of the male MBAs is higher than the average salary of female MBAs. H1: The average salary of the male MBAs is not higher than the average salary of female MBAs. #two sided test

library(MASS)
library(psych)

describe(placedfemale.df$Salary)

##    vars   n     mean       sd median  trimmed     mad min    max  range
## X1    1 127 193288.2 125857.6 220000 192598.1 99334.2   0 650000 650000
##     skew kurtosis       se
## X1 -0.12     0.17 11168.06

describe(placedmale.df$Salary)

##    vars   n     mean       sd median  trimmed   mad min    max  range skew
## X1    1 264 231484.9 142489.8 250000 229273.6 74130   0 940000 940000 0.31
##    kurtosis      se
## X1     2.05 8769.64

par(mfrow=c(1,2))
boxplot(placedfemale.df$Salary)
boxplot(placedmale.df$Salary)

Q.What is the average salary of male MBAs who were placed? Q.What is the average salary of female MBAs who were placed?

aggregate(dean.df$Salary, by=list(dean.df$Gender.B), FUN= mean)

##   Group.1        x
## 1       0 231484.8
## 2       1 193288.2

t.test(dean.df$Salary,dean.df$Gender.B,paired = TRUE)

## 
##  Paired t-test
## 
## data:  dean.df$Salary and dean.df$Gender.B
## t = 31.32, df = 390, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  205325.9 232830.0
## sample estimates:
## mean of the differences 
##                219077.9

Q.What is the p-value based on the t-test?

(t.test(dean.df$Salary,dean.df$Gender.B,paired = TRUE))$p.value

## [1] 1.642345e-108

Please interpret the meaning of the t-test, as applied to the average salaries of male and female MBAs.

It is observed that the avg. salary of placed males is more than avg. salary placed females.