Date: Feb 18, 2011 9:32 AM
Author: dstarnes@lawrenceville.org
Subject: Re: [ap-stat] when sigma is known

Dave,

There has been such an emphasis on this listserv about the mantra "z is
for proportions, t is for means" that we may have gone a little overboard!
The more careful mantra is probably something like "when doing inference,
z is for proportions and t is for means (unless we somehow know the
population sigma)". That parenthetical is important in questions about
determining sample size when planning a study in which students are
expected to use a given value that represents the population standard
deviation. And yes, there have been both free response and multiple
choice questions of that sort on the AP exam.

If a question is being posed about calculating a probability involving the
sampling distribution of x-bar, it's quite likely that a value will be
given for the population mean and standard deviation. In that setting
(assuming we have either a Normal population distribution or a large
sample size so the CLT applies), students should be using the standard
Normal (z) distribution to find the desired probability. Using the t
distribution might yield a similar answer, but there isn't a valid
theoretical reason to do so, which would probably mean that a student
wouldn't receive full credit for using t.

Hope this helps.

Daren Starnes
Math Department Chair & Master Teacher
The Lawrenceville School



david indelicato <dind@optonline.net>
02/18/2011 09:20 AM
Please respond to
david indelicato <dind@optonline.net>


To
"AP Statistics" <ap-stat@lyris.collegeboard.com>
cc

Subject
[ap-stat] when sigma is known






Hey stats teachers,

I came across a multiple choice question about a sampling distribution
for sample means in which a student is asked to compute an area. In the
problem, it is stated that the population standard deviation is known.
The question expects the student to use the z-distribution instead of
the t-distribution. The solution using z (.046) and the solution using
t (.050) are both given as choices. So if the student uses t, they will
get the wrong answer on this multiple choice question.

I was wondering, if this situation showed up in an open response
question and a student used t instead of z, would their solution be
close enough to get full credit? Is it wrong to use t when we know the
population standard deviation or just not as accuarate as using z?
Thanks in advance for any thoughts.

Dave Indelicato

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