Confidence Intervals
Why are these students stacking candy hearts? What
possible educational purpose can that serve?
Probably none, but they are having fun. This student will
never get all of those hearts in one stack.
This will work a lot better. Stacking candy seemed to
amused them.
The candy itself was left over from Valentine's Day and
was used in a previous class to illustrate confidence
intervals. We were trying to estimate the average number of
candy hearts in the individual bags. The sample itself was
not a random samplethe individual bags came from a couple
of big bags of little bags from a local store that had
discounted them to get rid of them. So the results may not
be valid, but the point was to show in a sweet, nonabstract
way how a procedure worked.
Each student got a couple of bags to count, and then we
entered the results into a spreadsheet. Using the sample
mean, the standard error, and a tvalue obtained from a
tvalue
calculator, we got an interval estimate, an estimate
that involved hearing, sight, touch, taste, and maybe even
smell. With a sample of 30 bags, we had a mean of 18.7 and a
standard deviation of 2.053592311. This implies a standard
error of 0.374932944. We know that if we take another sample
of 30 bags, we will probably not get the same as we got the
first time. Each time we take a sample, we almost always be
a bit too big or a bit too small.
The standard error is an estimate of how much we will be
off on average. Using that, we can construct an interval in
a way so that 95% of the time when we construct this
interval, we will get the true mean. For this example, we
would be 95% confident in the interval 17.9 to 19.5. We
cannot tell if the average per bag is 18 or 19, but we are
pretty sure it is not 17 or 20.
Except that one student spilled his candy on the floor.
He picked it up and counted it, but another student may have
added some bits to his pile. He got 26, which was the
highest of any student. If we include his bag, we change our
interval to 18.1 to 19.8. But should we count it?
I hope the story of this 100cents, fivesense experience
makes sense to you.
