Assignment Problem: Select a random sample using a table of random numbers (either one provided by your instructor or one from a website, such as "randomizer". Compute a statistic based on your sample, and compare it with the corresponding figure for the entire population. Here's how to proceed:
a. First, select a very small population for which you have a reasonably complete sampling frame. One possibility would be the listing of some characteristic of states in a U.S. Census Bureau publication, such as average income or population size. Another possible population would be the list of asking prices for houses advertised in your local paper.
b. Next, make a sampling frame, a numbered list of all the available elements in the population. If you are using a complete listing of all elements, as from a U.S. Census Bureau publication, the sampling frame is the same as the list. Just number the elements (states). If your population is composed of housing ads in the local paper, your sampling frame will be those ads that contain a housing price. Identify these ads, and then number them sequentially, starting with 1.
c. Decide on a method of picking numbers out of the random number table, such as taking every number in each row, row by row, or moving down or diagonally across the columns. Use only the first (or last) digit in each number if you need to select 1 to 9 cases or only the first (or last) two digits if you want 10 to 99 cases.
d. Pick a starting location in the random number table. It's important to pick a starting point in an unbiased way, perhaps by closing your eyes and then pointing to some part of the page.
e. Record the numbers you encounter as you move from the starting location in the direction you decided on in advance, until you have recorded as many random numbers as the number of cases you need in the sample. If you are selecting states, 10 might be a good number. Ignore numbers that are too large (or small) for the range of numbers used to identify the elements in the population. Discard duplicate numbers.
f. Calculate the average value in your sample for some variable that was measured (e.g., population size in a sample of states or housing price for the housing ads). Calculate the average by adding the values of all the elements in the sample and dividing by the number of elements in the sample.
g. Go back to the sampling frame, and calculate this same average for all the elements in the list. How close is the sample average to the population average?
h. Estimate the range of sample averages that would be likely to include 90% of the possible samples.