Starburst and Sampling - Case Notes

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Author - John Shepherd - Spring 2000

Case Materials: Six coffee cans contain the following Starburst candies:

The cans reside in John Shepherd's office (WSC 213) and can be borrowed as long as you promptly replace any candies that are eaten when you use them.   This can be done with any candy. Hard candy would be cheaper than Starburst.   Since they are handling the candy repeatedly, unwrapped candy is not suitable if you are going to let them eat any.

Teaching Notes :

Part One: Effects of Sample Size

Each student group is given a coffee can.   The cans are described as models of the real world, which is the student bodies of a number of universities.  Each candy represents a student and the color of a candy tells the student's year (as noted above).  You can, of course, make up any story.  Mine has been that I have a daughter about to go to college. I want to know something about the school’s retention in order to make a college choice.  Students might discuss retention and what it could say about a school.  Next discuss how to measure retention? %seniors? %freshmen?  In any case, % students in classes could give the required information (with some assumptions).   I have them estimate the percentage freshmen.

Groups are then asked to take repeated samples of different sizes as indicated by the layout of the data sheet (Word97) or (html).   Remember if you print the html version, you may need to remove the passworded URL from the top before you give it to the students.  They sample with replacement. For each sample they record the number and percentages of students in each class.  This is very quick for sample sizes of 5, but much slower and more tedious with samples of 40.  If you do this in a 50-minute class, you could shorten it by reducing the number of large samples.

When the students have finished counting, collate the estimates of all groups by sample size on the board.  [Last time I tried the high-tech version.  As the students worked, I recorded their estimates in an Excel spreadsheet that had frequency distributions drawn automatically and project them on the screen.]  From these it's pretty obvious that larger samples give a narrower range of estimates but they are more trouble to collect.

Part Two: Comparing Estimates

Now they are told that I am an over-protective father who, if he had his way, would send his daughter to a convent to keep her out of trouble (you can probably come up with something better than this).  Since that is not an option I want to send her to the school with the fewest boys.  Which of the coffee-can universities has the fewest boys?

How should we collect the sample?

• A large of 40 will give us the most reliable information.
• A sample stratified by classes would also be desirable if the % male were likely to differ among the classes.  I have them stratify their sample using the % for each class in their sample(s) of 40.  They will have to approximate so they end up with a sample of exactly 40 candies.

Each group figures out how many of each class to have in their stratified sample, collects their data, estimates the overall percentage of males in the student body, and put their estimate on the board.  When they have finished, you can ask which school I should send my poor daughter to.  Predictably, they recommend the school with the lowest estimated percentage and they can then be told that all the cans are then same.

• How could we have gotten different estimates of the same number?
• How different would the estimates have to be for you to conclude that the differences were not caused just by chance?
• Would you use different criteria for small samples than for large?
• etc. This is a good segue into Chapter 6.

If you do all of this, you'll have to keep things moving to fit it all into 75 minutes.