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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