Lecture 2

#set.seed() it makes a sure the seed is random.
#rnorm --- is the R function that simulates random variates having a specified normal distribution. 

#set.seed() makes sure te values are organizably random
set.seed(1)
sample1= rnorm(n= 10, mean= 20, sd= 2)
sample1

 [1] 18.74709 20.36729 18.32874 23.19056 20.65902 18.35906 20.97486 21.47665
 [9] 21.15156 19.38922

#gets the mean, rounded to 3 decimal places 
round (mean (sample1), 3)

[1] 20.264

#Creates a 2nd random seed
set.seed(2)
sample2= rnorm(n= 10, mean= 20, sd= 2)
sample2

 [1] 18.20617 20.36970 23.17569 17.73925 19.83950 20.26484 21.41591 19.52060
 [9] 23.96895 19.72243

round (mean (sample2), 3)

[1] 20.422

#generate random samples for the same characteristics of the seed for # 1-100.
#mode: 'numeric' makes sure the value are read as numbers
sample_means= vector(mode= "numeric")

for(i in 1:100){
  set.seed(i)
  sample_means= c(sample_means, round (mean(rnorm(n= 10, mean= 20, sd= 2)), 2))
}

#Visualizes the datset. 
plot (sample_means, xlab= "Sample", ylab= "Xbar", yaxt = "n") +
axis(2, at=seq(18,22,0.5), labels=seq(18,22,0.5)) +
abline(h= 20)

numeric(0)

What changes if each sample has 50 values instead of 10? In other words, what changes if the sample size is increased from 10 to 50?

Let’s generate 100 samples each with 50 values, for each sample let’s compute the sample mean, and let’s compare all 100 samples means to the population mean of 20. - The more data points you have the more it relates/ looks like the normal distribution.

#instead of a =10, a =50
sample_means2= vector(mode= "numeric")

for(i in 1:100){
  set.seed(i)
  sample_means2= c(sample_means2, round (mean(rnorm(n= 50, mean= 20, sd= 2)), 2))
}

#Visualize the new datset
#n= the # of datapoints
#yaxt = making sure th 'n' values are being spread in the y.

#axis(, , )
#Syntax:axis(side, at=NULL, labels=TRUE)
#Parameters
#side: It defines the side of the plot the axis is to be drawn on possible values such as below, left, above, and right. 
#at: Point to draw tick marks
#labels: Specifies texts for tick-mark labels.

#side = 2 because there are 2 dimensions. (x,y)



plot (sample_means2, xlab= "Sample", ylab= "Xbar", yaxt = "n") +
axis(2, at=seq(18,22,0.5), labels=seq(18,22,0.5))+
abline(h= 20)

numeric(0)