Question

Use R studio to do it I need the code, thx.

Write your own function, called go_mean(). The user will provide a vector and the number of repetitions for the simulation. Your function should:
- Create an empty vector
- Draw a sample the same size as the vector, selecting from the vector itself, with replacement. - Compute the mean of the vector, and store it in the empty vector.

- Repeat the steps above n times.
- Compute an 80% confidence interval of the vector of means.
- Print the interval on the console so that it looks something like this: "Lower limit = value, Upper

limit = value", where the values are rounded to 2 decimal places.

Test your new function by creating a vector of 8000 z scores, and applying your function with 1000 reps

Answer 1

80% confidence interval is level of significance of

The critical value of z is

Using standard normal table/R we get the critical value as

If is the mean of vector of means then 80% confidence interval is

where is the standard error of mean, which is the sample standard deviation of vector of means

R code to implement all these (all statements starting with # are comments)

get the following output

Code in text format is below

go_mean<-function(x,n){

#create an empty vector to hold sample mean

xbar<-numeric(n)

for (i in 1:n) { #repeat n times

#Draw a sample the same size as the vector, with replacement

s<-sample(x,length(x),replace=TRUE)

#Compute the mean of the vector

xbar[i]<-mean(s)

}

#Compute an 80% confidence interval of the vector of means

cl<-80

alpha<-1-cl/100

zcrit<-qnorm(alpha/2,0,1,lower.tail=FALSE)

#get the statndard error of mean

se<-sd(xbar)

#get the lower limit

ll<-mean(xbar)-zcrit*se

#get the upper limit

ul<-mean(xbar)+zcrit*se

sprintf('Lower limit =%.2f, Upper limit = %.2f ',ll,ul)

}

#set the random seed

set.seed(123)

#create a vector of 8000 z scores

z<-rnorm(8000,0,1)

#call the function for n=1000 reps

go_mean(z,1000)