Q1: 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 (see lab keys for examples).

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))

plot(density(Exam1Q1$BS))

agostino.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

Summary: The dataset 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.