Question

Write a R code for the following

Using the SATGPA data set in Stat2Data package. Test by using α= .05.

1) Create the following three variables and then print out all the six variables. Create a new variable “SAT”, which is the sum of MathSAT and VerbalSAT. Create second new variable “SATLevel”, and assign the value of “SATLevel” as 1 when SAT<=1100, 2 when 11001300. Create third new variable “GPALevel” and assign the value of “GPALevel” as 1 when GPA<=2.8, 2 when 2.83.5 Print out all the data in the descending order of their GPALevel and the ascending order of their SAT when GPALevel is the same.

2) Use the Chi-Square test to conclude if the SATLevel and GPALevel are independent.

3) Compute the mean and variance of “GPA” for each level of “GPALevel”, and compute the correlation matrices for the four variables: MathSAT, VerbalSAT, GPA and SAT.

4) Do the data provide sufficient evidence to indicate that the mean of MathSAT is significantly greater than the mean of VerbalSAT.

5) Test if the proportion of MathSAT greater than VerbalSAT is 0.6.

Answer 1

Below is the R code of operations performed on Stat2Data package.

# Installing the package and loading the data

install.packages("Stat2Data")

library(Stat2Data)

data("SATGPA")

head(SATGPA)

# PART 1) Creating the given three variables

SATGPA$SAT <- SATGPA$MathSAT + SATGPA$VerbalSAT

SATGPA$SATLevel <- ifelse(SATGPA$SAT <= 1100, 1, 2)

SATGPA$GPALevel <- ifelse(SATGPA$GPA <= 2.8, 1, 2)

# Arranging data based on GPALevel and SAT

SATGPA[order(-SATGPA$GPALevel, SATGPA$SAT),]

# PART 2)

# Chi-square test to conclude the two variable SATLevel and GPALevel are independent.

chisq.test(SATGPA$SATLevel, SATGPA$GPALevel, correct = FALSE)

# Pearson's Chi-squared test

# data: SATGPA$SATLevel and SATGPA$GPALevel

# X-squared = 0.050526, df = 1, p-value = 0.8221

# PART 3)

# Finding mean and variance of GPA for each GPALevel.

aggregate(SATGPA$GPA, by = list(SATGPA$GPALevel), FUN = mean)

aggregate(SATGPA$GPA, by = list(SATGPA$GPALevel), FUN = var)

# Correlation matrix of the given dataset

cor(SATGPA)

# PART 4)

# Performing t-test to compare the mean of two given variable.

t.test(SATGPA$MathSAT, SATGPA$VerbalSAT, conf.level = 0.95)

# Welch Two Sample t-test

# data: SATGPA$MathSAT and SATGPA$VerbalSAT

# t = 2.2466, df = 45.753, p-value = 0.02954

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

# 95 percent confidence interval:

# 5.5836 101.9164

# sample estimates:

# mean of x mean of y

# 619.1667 565.4167

Code screenshot

1 # Installing the package and loading the data 2 install.packages C"stat2Data") 3 library(Stat2Data) 4 data("SATGPA" 5 head(SATGPA) 6 # PART 1) Creating the given three variables 7 SATGPASSATSATGPASMathSAT SATGPASVerbalSAT 8 SATGPASSATLevel <-ifel se (SATGPASSAT 1100, 1, 2) <= 9 SATGPASGPAL evel <-ifelse(SATGPASGPA <=2.8, 1, 2) 10 # Arranging data based on GPAL evel and SAT 11 SATGPA[order C-SATGPASGPALevel, SATGPASSAT) ,] 12 # PART 2) 13 # Chi-square test to conclude the two variable SATL evel and GPAL evel are independent. 14 chísq.test(SATGPASSATL evel, SATGPASGPAL evel, correct= FALSE) 15 # Pearson's Chi-squared test 16 17 # data: SATGPASSATL evel and SATGPASGPAL evel 18 # X-squared = 0.050526, df = 1, p-value = 0.8221 19 20 #PART3) 21 # Finding mean and variance of GPA for each GPAL evel. 22 aggregate(SATGPASGPA byist (SATGPASGPAL evel), FUNmean) 23 aggregate(SATGPASGPA byist (SATGPASGPAL evel), FUNvar) 24 # correlation matrix of the given dataset 25 cor (SATGPA,) 26 #PART4) 27 # Performing t-test to compare the mean of two given variable. 28 t. test(SATGPASMathSAT, SATGPASVerbal SAT, conf. Îevel =0.95) 29 30 # Welch Two Sample t-test 31 32 # data: SATGPASMathSAT and SATGPASverba1SAT 33 #t-2.2466 , df-45.753, p-value-0.02954 34 # alternative hypothesis: true difference in means is not equal to 0 35 # 95 percent confidence interval: 36 # 5.5836 101.9164 37 # sample estimates: 38 # mean of x mean of y 39 #619.1667 565.4167 40
Output screenshot

> head (SATGPA) MathSAT VerbalSAT GPA SAT SATLevel GPALevel 580 670 680 630 620 580 420 2.90 1000 530 2.83 1200 540 2.90 1220 640 3.30 1270 630 3.61 1250 550 2.75 1130 > chísq.test(SATGPASSATL evel, SATGPASGPALevel, correct = FALSE) Pearson's Chi-squared test data SATGPA$SATL evel and SATGPASGPALevel X-squared = 0.050526, df = 1, p-value = 0.8221