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
andmns3
.] - Repeat the previous calculations for samples of n=4. [Copy-and-paste and use
num4
andmns4
.]
Mean | St. Dev. | |
---|---|---|
POPULATION | ||
n=2 | ||
n=3 | ||
n=4 |
- What symbols should be placed on the mean and standard deviation of the population shown in the first row of your table.
- How did the means of the sample means change with increasing n?
- How did the three means of sample means (i.e., from n=2, 3, and 4) compare to the population mean?
- What should the standard deviation of the sample means calculated above be called?
- How did the three standard deviations of sample means compare to the population standard deviation?
- How did the standard deviations of the sample means change with increasing n?