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Topic: Chuck Biehl's question
Replies: 0

 Rudy Wiegand Posts: 18 Registered: 12/6/04
Chuck Biehl's question
Posted: Jan 7, 1997 4:57 PM

:Speaking of having problems, I seem to have developed a mental block on
:being able to get the kids to understand applying concepts to
:calculations in this context. Here's an example of a problem which has
:been condensed a bit:
:"If 113 of 130 people in an SRS respond favorably, construct a 95%
:confidence interval for the population." For some stupid reason (I
:hope), I'M STUCK!!!

I address two areas: first the question itself and second the application of
concepts by the student.

I too have difficulty with the question. Assuming we are discussing a
CI for the population PARAMETERS, several question arise. (1)Are the
responses random? If one group can be expected to respond with a bias and
that group is more likely to respond than others, then the results are
biased. At this level, I feel most of us would allow/suggest the assumption
of random responses; but, it does deserve discussion. (2) What is the
population? In particular, how big is it? If it is 130, no confidence
interval is needed--you have your parameter(assuming it is the proportion
favorable). If it is relatively small, say less than 1300, or so, you may
need a finite correction factor(hypergeometric model)to a standard binomial
model. If larger,(or using the correction factor) one might use the
standard normal approximation to the binomial proportion, p. (3) What model
is appropriate? Under the assumption of random responses, I'd probably
choose the binomial.

The more difficult question was deliberately held for last because I
suspect each of us tries to discuss the ideas in the above paragraph. I
believe part of the students problem is that we reveal so much to them that
our caveats confuse them OR that they intuitively are aware of some of the
real world problems and cannot believe a specific model applies. In the
problem cited, there are valid reasons to believe the binomial model may not
apply. The student, perhaps subconsciously, is aware of this--particularly
if we have stressed that the responses must be random. Add to this the
concept that we are APPROXIMATING one distribution with another and students
already uncertain as to the appropriateness of the model, suddenly are faced
with the intuitive feeling that APPROXIMATING an uncertain model is a fool's
errand. Fear (perhaps too much information) of being incorrect makes them
hesitate.
I try to avoid this(only somewhat effectively) by stressing that we are
choosing a model and we must always examine the reasonableness of our
model's assumptions. I further stress that most of the models we study in
THIS course are fairly forgiving of minor deviations from some of the
assumptions. I frequently require that students provide me a discussion of
the model's assumptions for one, or two, homework problems each night. They
are asked to pick those which gave them the greatest intellectual
difficulty. This discussion is to include whether they are certain each
assumption of the model holds OR would they be willing to say that THEY
expect the assumption to be "reasonable" for the given situation. In our
case, we have discussed the discrete models: binomial, uniform, poisson,
hypergeometric, and geometric(and, of course, general tabulated
distributions).