Assume that the above 2022 admission data is the population is known

Use the R program and the codes given in Lectures and Discussions to answer the questions below

l.Points=1+(1+1)=3.

(a)What is the numerical value of the population size N?

(b)Calculate the population mean and the population variance using the equations (2.8) and (2.9) in Text. Copy and paste the R code and output as the answer.

ll.Points=1+(1+1)=3.

(a) Draw a simple random sample without replacement of sizen=3. Copy and paste the R code and output as the answer.

(b)Calculate the sample mean and the sample variance using the equations(2.11)and(2.13)in Text Copy and paste the R code and output as the answer

lll.Points=(1+1)+(0.5+0.5+0.5+0.5)=4.

(a)Calculate the variance and standard error of the sample mean using the equations(2.14)and(2.15 in Text.Copy and paste the R code and output as the answer

(b)Calculate the difference between the sample mean and population mean. What is the meaning of the sign of the difference? What is the interpretation of the magnitude of the difference? Express the difference in the standard error unit i.e as a constant time of the standard error and specify the numerical value of it.