The data below represents the yearly earnings (in $1000s of dollars) that high school and college (BS) graduates earn at a small firm. Determine if there is any difference in pay for the two groups: Be sure to include a complete analysis (i. e., all assumptions checked and full understanding of effects garnered) and a clear summary with all needed statistical details included.

library(moments)

library(readxl)

Exam1Q1 <- read_excel("Exam1Q1.xlsx")

View(Exam1Q1)

## Warning in system2("/usr/bin/otool", c("-L", shQuote(DSO)), stdout = TRUE):

## running command ''/usr/bin/otool' -L '/Library/Frameworks/R.framework/

## Resources/modules/R_de.so'' had status 1

plot(density(Exam1Q1$Highschool))

gostino.test(Exam1Q1$Highschool)

##  

##  D'Agostino skewness test

##  

## data:  Exam1Q1$Highschool

## skew = -0.24041, z = -0.69269, p-value = 0.4885

## alternative hypothesis: data have a skewness

agostino.test(Exam1Q1$BS)

##  

##  D'Agostino skewness test

##  

## data:  Exam1Q1$BS

## skew = 0.53467, z = 1.49330, p-value = 0.1354

## alternative hypothesis: data have a skewness

anscombe.test(Exam1Q1$Highschool)

##  

##  Anscombe-Glynn kurtosis test

##  

## data:  Exam1Q1$Highschool

## kurt = 2.56950, z = -0.29677, p-value = 0.7666

## alternative hypothesis: kurtosis is not equal to 3

anscombe.test(Exam1Q1$BS)

##  

##  Anscombe-Glynn kurtosis test

##  

## data:  Exam1Q1$BS

## kurt = 3.6449, z = 1.2599, p-value = 0.2077

## alternative hypothesis: kurtosis is not equal to 3

t.test(Exam1Q1$Highschool,Exam1Q1$BS, var.equal = T)

##  

##  Two Sample t-test

##  

## data:  Exam1Q1$Highschool and Exam1Q1$BS

## t = 0.16929, df = 76, p-value = 0.866

## alternative hypothesis: true difference in means is not equal to 0

## 95 percent confidence interval:

##  -1.131669  1.341926

## sample estimates:

## mean of x mean of y  

##  39.51282  39.40769

Explanation:

Summary:

The data set include two dependent variables which states High School annual earnings and BS annual earnings in the same small firm. Firstly, I used density plot function to view the distribution of two sets of variables. Secondly, I tested the skewness and kurtosis.Skewness of High School is -0.24041 which is left tail. Skewness of BS is 0.53476 which is right tail.Kurtosis of High School is 2.5695 which lower than 3 is platykurtic. Kurtosis of BS is 3.6449 which larger than 3 is leptokurtic. Thirdly, the sample population is 39 for each and has unknow standard deviation, so that I’m going to use t-test to perform the comparing analysis. The result shows p-value which equal to 0.866 is larger than significant value(alpha = 0.05). To the concludsion, there is no difference between yearly earnings of High School and of BS at a small firm.