Dean’s Dillema :

On January 16, 2014, Easwaran Iyer, Dean of Jain University’s business school (B-school), was preparing for the meeting that he had scheduled the next day with the Admissions Committee of the B-school. Iyer wanted to ensure that the right set of students were admitted to their Master of Business Administration (MBA) program, but he was not sure about the parameters to identify ideal students for this program. Jain University received applications for the MBA program from across India and admitted approximately 400 students to this program every year. There had been a steady increase in the number of applications received by Jain University over the years. The university had reached a stage where they could be very selective in choosing students for the MBA program. Iyer was sure that the number of applicants for Jain University’s MBA program would continue to increase as long as they selected good students and placed them successfully in careers in their chosen domain.

A short view of the data set

deans.df <- read.csv(paste("DeansDilemma.csv", sep=""))

head(deans.df)
##   SlNo Gender Gender.B Percent_SSC Board_SSC Board_CBSE Board_ICSE
## 1    1      M        0       62.00    Others          0          0
## 2    2      M        0       76.33      ICSE          0          1
## 3    3      M        0       72.00    Others          0          0
## 4    4      M        0       60.00      CBSE          1          0
## 5    5      M        0       61.00      CBSE          1          0
## 6    6      M        0       55.00      ICSE          0          1
##   Percent_HSC Board_HSC Stream_HSC Percent_Degree         Course_Degree
## 1       88.00    Others   Commerce          52.00               Science
## 2       75.33    Others    Science          75.48 Computer Applications
## 3       78.00    Others   Commerce          66.63           Engineering
## 4       63.00      CBSE       Arts          58.00            Management
## 5       55.00       ISC    Science          54.00           Engineering
## 6       64.00      CBSE   Commerce          50.00              Commerce
##   Degree_Engg Experience_Yrs Entrance_Test S.TEST Percentile_ET
## 1           0              0           MAT      1          55.0
## 2           0              1           MAT      1          86.5
## 3           1              0          None      0           0.0
## 4           0              0           MAT      1          75.0
## 5           1              1           MAT      1          66.0
## 6           0              0          None      0           0.0
##   S.TEST.SCORE Percent_MBA  Specialization_MBA Marks_Communication
## 1         55.0       58.80      Marketing & HR                  50
## 2         86.5       66.28 Marketing & Finance                  69
## 3          0.0       52.91 Marketing & Finance                  50
## 4         75.0       57.80 Marketing & Finance                  54
## 5         66.0       59.43      Marketing & HR                  52
## 6          0.0       56.81 Marketing & Finance                  53
##   Marks_Projectwork Marks_BOCA Placement Placement_B Salary
## 1                65         74    Placed           1 270000
## 2                70         75    Placed           1 200000
## 3                61         59    Placed           1 240000
## 4                66         62    Placed           1 250000
## 5                65         67    Placed           1 180000
## 6                70         53    Placed           1 300000
placed.df <- deans.df[which(deans.df$Placement_B == '1'),]

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

table(placed.df$Gender)
## 
##   F   M 
##  97 215
aggregate(deans.df$Salary, by=list(deans.df$Gender), FUN=mean)
##   Group.1        x
## 1       F 193288.2
## 2       M 231484.8

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

mean(placed.df$Salary[which(placed.df$Gender=='M')])
## [1] 284241.9

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

mean(placed.df$Salary[which(placed.df$Gender=='F')])
## [1] 253068

here most of the male student are placed and have much salary than female students.

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.”

male.df<- placed.df$Salary[which(placed.df$Gender=='M')]
female.df<- placed.df$Salary[which(placed.df$Gender=='F')]
t.test(male.df,female.df)
## 
##  Welch Two Sample t-test
## 
## data:  male.df and female.df
## t = 3.0757, df = 243.03, p-value = 0.00234
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  11209.22 51138.42
## sample estimates:
## mean of x mean of y 
##  284241.9  253068.0

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

According to the test p value is : .00234

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

mean of male : 284241.9

mean of female: 253068.0