Basic Statistics - Old Questions

3. The following data represent the number of days absent of IT faculty per semester in a population of 4 faculties in an academic institute.

a) Select all possible samples of size n = 2 with replacement, and construct the sampling distribution of mean.

b) Compare the population mean and mean of all sample means. Are they equal?

c) Compare the shape of the population data and shape of the sampling distribution. Do you find any differences? Comment.

d) Compare the population standard deviation and standard deviation of sample means and explain your observation.