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SIO 272 Homework questions: -subject line “statsHW1”

Review: Writing FOR Loops

Using a simulaiton to generate a distribution based on a fake test statistic. Kayla’s test. The equation is: = sum(Z*10)^2 where Z is the normal distribution (can be specified using th rnorm function below)

Let’s start with empty vectors to put the results into first.

#generate empty vectors to place results from 1000 simulations
#the rep() function makes it easy to create vectors of (x,y) dimensions. Using the NA placeholder tells R to fill the vector with empty spaces, and will default to 1 in the case of the rep() function.
norm1 <- rep(NA,1000)
norm3 <- rep(NA,1000)
norm30 <- rep(NA,1000)
norm100 <- rep(NA,1000)

#write a for loop that simulates these draws 1000 times and places them into the empty vectors.
for(i in 1:length(norm1)){
norm1[i] <- sum(rnorm(1,m=0,sd=1)*10)^2    
norm3[i] <- sum(rnorm(3,m=0,sd=1)*10)^2   
norm30[i] <- sum(rnorm(30,m=0,sd=1)*10)^2   
norm100[i] <- sum(rnorm(100,m=0,sd=1)*10)^2   
}

Generate a plot to see these.

#OPTION 1 - use the PLOT function and draw lines over the first one.
plot(density(norm1), col='blue', main="Kayla's distribution", lwd=2)
lines(density(norm3),col='red',lwd=2)
lines(density(norm30),col='black',lwd=2)
lines(density(norm100),col='green',lwd=2)

Formulas in R markdown

X-bar \(\overline{X}\)

Y-hat \(\hat{Y}\)

Basic Fraction \(\frac{X}{Y}\)

Formula Fraction \(\frac{{X} - {\overline{X}}} {sd}\)