Question

Take a simple random sample from a box of 100000 tickets, the box contains 50% 0's and 50% 1's. If you draw 2500 and 25000 tickets respectively without replacement, using R studio, do 10000 replications for each part, and find the SD of all the sample percent. Moreover, make a histogram of the 10000 sample percent for each part (2 histograms).

Answer 1

R CODE:

n=100000
x=c()
S1=c()
S2=c()

for(k in 1:10000)
{
   #creating the box of 100000 tickets
   x=sample(c(0,1),size=n,replace=TRUE)
  
   #drawing sample of size 2500 without replacement
   A=sample(x,size=2500,replace=FALSE)
   #taking sum
   S1[k]=sum(A)

   #drawing sample of size 25000 without replacement
   B=sample(x,size=25000,replace=FALSE)
   #taking sum
   S2[k]=sum(B)
  
}
sd(S1)
sd(S2)
par(mfrow=c(1,2))
hist(S1,main="Histogram(2500)")
hist(S2,main="Histogram(25000)")

RESULT:

> sd(S1)
[1] 24.81566
> sd(S2)
[1] 79.15947

GRAPH: