Dean’s Dilemma Week 2 Day 1

This is a case study of “Dean’s Dilemma: Selection of Students for the MBA Program” to understand the issues faced by the Dean. The job of the Admissions Committee was to admit the best candidates from among the available lot. The committee considered an applicant’s academic grades and discipline, entrance test score, and work experience (if any). It also judged candidates by their performance in the personal interview. Similar to most MBA admissions committees, the team had the mandate to build a diverse batch. Their objective was to put together a group of different yet similar candidates. The admissions team wanted to understand whether a student’s academic record would have any reflection on the placement status. What could be the possible criteria for assessing/selecting a student who could get placed in a good role, with a good pay packet?

TASK 3 (a)

Recall the Data - Dean’s Dilemma.csv data file associated with the case “A Dean’s Dilemma: Selection of Students for the MBA Program” that has been analyzed on WEEK 1, DAY 6.

setwd("D:/manipal-year2/internship/IIML_dataAnalytics/Datasets")
deandilemma.df <- read.csv(paste("DeansDilemmaData.csv",sep=""))
View(deandilemma.df)

TASK 3 (b)

Use R to create a table showing the average salary of males and females, who were placed. Review whether there is a gender gap in the data. In other words, observe whether the average salaries of males is higher than the average salaries of females in this dataset.

placed.df <- deandilemma.df[which(deandilemma.df$Placement_B==1),]
aggregate(placed.df$Salary,by=list(GENDER  = placed.df$Gender),mean)
##   GENDER        x
## 1      F 253068.0
## 2      M 284241.9

Since there is almost a difference of 30,000 in the average salaries of male and female, there is a gender gap in the data.

TASK 3 (c)

Use R to run a t-test to test the following hypothesis: H1: The average salary of the male MBAs is higher than the average salary of female MBAs

t.test(Salary ~ Gender,data=deandilemma.df)
## 
##  Welch Two Sample t-test
## 
## data:  Salary by Gender
## t = -2.69, df = 278.55, p-value = 0.007577
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -66149.06 -10244.26
## sample estimates:
## mean in group F mean in group M 
##        193288.2        231484.8

The t-test shows that the p-value is less that 0.05 and hence, there is a relationship between the gender of the student and the salary obtained. The mean values prove that average salary of male MBAs is higher than those of female MBAs.

TASK 3 (d)

List of questions based on “A Dean’s Dilemma: Selection of Students for the MBA Program”

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

placed.df <- deandilemma.df[which(deandilemma.df$Placement_B==1),]
aggregate(placed.df$Salary,by=list(GENDER  = placed.df$Gender),mean)
##   GENDER        x
## 1      F 253068.0
## 2      M 284241.9

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

aggregate(placed.df$Salary,by=list(GENDER  = placed.df$Gender),mean)[2,2]
## [1] 284241.9

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

aggregate(placed.df$Salary,by=list(GENDER  = placed.df$Gender),mean)[1,2]
## [1] 253068

4.Submit 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.”

t.test(Salary ~ Gender,data=deandilemma.df)
## 
##  Welch Two Sample t-test
## 
## data:  Salary by Gender
## t = -2.69, df = 278.55, p-value = 0.007577
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -66149.06 -10244.26
## sample estimates:
## mean in group F mean in group M 
##        193288.2        231484.8

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

From the output of t-test done above, the p-value comes out to be 0.007577.

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

The small p-value indicates that we can reject the null hypothesis that there is no significant difference in salaries between males and females.

The t-test shows that the p-value is less that 0.05 and hence, there is a relationship between the gender of the student and the salary obtained. The mean values prove that average salary of male MBAs is higher than those of female MBAs.