A Two-Stage Cluster Sample

library(tidyverse)
library(openintro)

The Research Question

What is the average class size at UTSA? Many students complain about large classes, many universities brag about their small classes. Let’s put a number on it.

SRS of 5 Clusters

sample(1:132, 5, replace=FALSE)

## [1]  74  28 128  66   3

## Output [1] 120  78  74  47  11
## 11=ART 47=ENT 74=IDE 78=KIN 120=SPE

The output produced by the simple random sampling function corresponded to the following five class subjects: Art, Entrepreneurship, Interior Design, Kinesiology, and Special Education.

Import Data

ARTraw <- read.csv("C:/Users/Savanna.DESKTOP-0OJMFCH/Downloads/ART.CSV")
ENTraw <- read.csv("C:/Users/Savanna.DESKTOP-0OJMFCH/Downloads/ENT.CSV")
IDEraw <- read.csv("C:/Users/Savanna.DESKTOP-0OJMFCH/Downloads/IDE.CSV")
KINraw <- read.csv("C:/Users/Savanna.DESKTOP-0OJMFCH/Downloads/KIN.CSV")
SPEraw <- read.csv("C:/Users/Savanna.DESKTOP-0OJMFCH/Downloads/SPE.CSV")
library(tidyverse)

Clean Data

ART <- ARTraw[!(ARTraw$Status=="CANCELED"| ARTraw$Title=="Independent Study"| ARTraw$Title=="Internship in the Visual Arts"| ARTraw$Course>=5000),]

ENT <- ENTraw[!(ENTraw$Status=="CANCELED"| ENTraw$Title=="Independent Study"| ENTraw$Title=="Internship in Entrepreneurship"| ENTraw$Course>=5000),]

IDE <- IDEraw[!(IDEraw$Status=="CANCELED"| IDEraw$Title=="Independent Study"| IDEraw$Title=="Practicum/Internship"| IDEraw$Course>=5000),]

KIN <- KINraw[!(KINraw$Status=="CANCELED"| KINraw$Title=="Independent Study"| KINraw$Title=="Internship in Kinesiology"| KINraw$Title=="Honors Thesis"| KINraw$Course>=5000),]

SPE <- SPEraw[!(SPEraw$Status=="CANCELED"| SPEraw$Title=="Independent Study"| SPEraw$Course>=5000),]

Summarizing Data

#ART Data
ARTrows<- count(ART) #cluster size of 74
#RSS of 3 independent estimates
sample(1:10, 3, replace = FALSE) #original output [1] 10  2  5

## [1] 1 9 7

a<- c(10, 20) 
b<- c(2, 12) 
c<- c(5, 15) 
amean <- mean(a)
bmean <- mean(b)
cmean <- mean(c)
ARTmean <- c(amean, bmean, cmean)
ARTvar <- var(ARTmean)
ARTsum <- sum(ART$Enrolled)

#ENT Data
ENTrows<- count(ENT) #cluster size of 5
ENTmean<- mean(ENT[,"Enrolled"])
ENTvar <- var(ENT[,"Enrolled"])
ENTsum <- sum(ENT$Enrolled)

#IDE Data
IDErows<- count(IDE) #cluster size of 8
IDEmean<- mean(IDE[,"Enrolled"])
IDEvar <- var(IDE[,"Enrolled"])
IDEsum <- sum(IDE$Enrolled)

#KIN Data
KINrows<- count(KIN) #cluster size of 53
#RSS of 3 independent estimates
sample(1:10, 3, replace = FALSE) #output [1] 15  2  3

## [1] 10  5  9

x<- c(15, 25) 
y<- c(2, 12) 
z<- c(3, 13) 
xmean <- mean(x)
ymean <- mean(y)
zmean <- mean(z)
KINmean<- c(xmean, ymean, zmean)
KINvar<- var(KINmean)
KINsum<- sum(KIN$Enrolled)

#SPE Data
SPErows<- count(SPE) #cluster size of 11
SPEmean<- mean(SPE[,"Enrolled"])
SPEvar<- var(SPE[,"Enrolled"])
SPEsum<- sum(SPE$Enrolled)

Print Values

ARTmean

## [1] 15  7 10

ARTvar

## [1] 16.33333

ENTmean

## [1] 26.2

ENTvar

## [1] 305.2

IDEmean

## [1] 20.875

IDEvar

## [1] 127.8393

KINmean

## [1] 20  7  8

KINvar

## [1] 52.33333

SPEmean

## [1] 32.27273

SPEvar

## [1] 364.6182

Estimate of Mean Class Size

class <- c(ARTmean, ENTmean, IDEmean, KINmean, SPEmean)
t.test(class, conf.level = 0.95)

## 
##  One Sample t-test
## 
## data:  class
## t = 5.3266, df = 8, p-value = 0.0007054
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##   9.22117 23.30055
## sample estimates:
## mean of x 
##  16.26086

The t-test provides the average class size to have 16 students. There is a 95% probability that the size of any given Undergraduate class at UTSA would consist of 9 to 23 students enrolled. This estimate does exclude internships, independent studies, and honors thesis.

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