Construct Sampling Distributions

In this exercise, you will construct actual sampling distributions for different size samples from a very simple population. The very simple population use here is five individuals with the following values – 12, 14, 16, 18, 20. Perform the bulleted steps below and then answer the questions further below.

  • Compute the center and dispersion (to three decimals) of this population. Write results in table further below.
popn <- c(12,14,16,18,20)      # creates population
Summarize(popn,digits=3)       # population summaries
  • Identify all possible samples of n=2 from this population. [Look at these to make sure that they make sense to you.]
( nums2 <- combn(popn,2) )     # all combos of n=2 from popn (look at verticals)
  • Compute the mean for each sample. [Look at these to make sure that they make sense to you.]
( mns2 <- combn(popn,2,mean) ) # mean of all combos of n=2
  • Compute the mean and standard deviation of all 10 sample means. Write the results in the table further below.
Summarize(mns2,digits=3)       # summarized mean/sd of means
  • Repeat the previous four calculations for samples of n=3. [Copy-and-paste your code for n=2 but change the names to num3 and mns3.]
  • Repeat the previous calculations for samples of n=4. [Copy-and-paste and use num4 and mns4.]
  Mean St. Dev.
POPULATION    
n=2    
n=3    
n=4    
  1. What symbols should be placed on the mean and standard deviation of the population shown in the first row of your table.
  2. How did the means of the sample means change with increasing n?
  3. How did the three means of sample means (i.e., from n=2, 3, and 4) compare to the population mean?
  4. What should the standard deviation of the sample means calculated above be called?
  5. How did the three standard deviations of sample means compare to the population standard deviation?
  6. How did the standard deviations of the sample means change with increasing n?