A Dean’s Dilemma: Selection of Students for the MBA Program.

Reading

setwd("C:/Users/Shreyas Jadhav/Downloads")  
dilemma <- read.csv(paste("Deans_Dilemma.csv",sep="."))
View(dilemma)

Extended Analysis

(3d)List of Questions and Solutions

(1)R code that creates a table showing the mean salary of males and females, who were placed.

placed <- dilemma[which(dilemma$Placement=='Placed'),]
mytable <- aggregate(Salary~Gender, data=placed, mean)
mytable
##   Gender   Salary
## 1      F 253068.0
## 2      M 284241.9

(2)Average salary of male MBAs who were placed.

mytable
##   Gender   Salary
## 1      F 253068.0
## 2      M 284241.9

Therefore, the average salary of male MBAs who were placed is INR 284241.9

(3)Average salary of female MBAs who were placed.

mytable
##   Gender   Salary
## 1      F 253068.0
## 2      M 284241.9

Therefore, the average salary of female MBAs who were placed is INR 253068.0

(4)R code to run a t-test for the Hypothesis “The average salary of the male MBAs is higher than the average salary of female MBAs.”

placed <- dilemma[which(dilemma$Placement=='Placed'),]
log.transformed.Salary = log(placed$Salary)
t.test(log.transformed.Salary ~ placed$Gender, var.equal=TRUE)
## 
##  Two Sample t-test
## 
## data:  log.transformed.Salary by placed$Gender
## t = -2.8142, df = 310, p-value = 0.005203
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.17482594 -0.03094897
## sample estimates:
## mean in group F mean in group M 
##        12.40435        12.50723

(5)p-value based on the t-test.

As shown in the solution for 4th question, t = -2.8142, df = 310, p-value = 0.005203. Therefore the p-value = 0.005203

(6)Interpret the meaning of the t-test, as applied to the average salaries of male and female MBAs.

Results:

  1. From (1),(2)and (3), the average salary of male MBAs who were placed (INR 284241.9) is more than the the average salary of female MBAs who were placed (INR 284241.9).

Null Hypothesis: “There is no significant difference in the average salary of male and female MBAs who were placed.”

  1. From (4), p-value = 0.005203 i.e p-value < 0.05 which mean we reject the Null Hypothesis and accept the alternative Hypothesis.

Alternative Hypothesis: “There is a significant difference in the average salary of male and female MBAs who were placed is equal.”

  1. Therefore, the t-test shows that There is a significant difference in average salary of males MBAs and female MBAs, who were placed. The average salary of the male MBAs is higher than the average salary of female MBAs