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Re: [apstat] when sigma is known
Posted:
Feb 18, 2011 9:32 AM


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 xbar, 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" <apstat@lyris.collegeboard.com> cc
Subject [apstat] 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 zdistribution instead of the tdistribution. 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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