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Topic: Exam message? (y/n) y
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Bob Hayden

Posts: 2,384
Registered: 12/6/04
Exam message? (y/n) y
Posted: May 7, 1997 8:18 PM
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----- Forwarded message from Sanderson Smith -----

I realize that problem #5 is an ideal t-distribution situation (working with
either the difference column or the comparison of two means). However, would
this approach be acceptable if it was presented on the test?
Looking at the differences, there are five positive differences and three
negative differences. (and one difference of zero). If there is no difference
in the ovens, then the number of positive differences would be "expected" to
equal the number of negative differences. The probability that one would get
five or more positive differences is
(8C5 + 8C6 + 8C7 + 8C8)x(.5)^8, which I calculate to be about 36%. In other
words, there is not strong evidence to suggest a difference in the ovens. Is
this any better or worse than using the t-distribution?

----- End of forwarded message from Sanderson Smith -----

I didn't check your arithmetic or setup but what you are trying to do
is a legitimate test called the sign test. It tests whether the
population MEDIAN is 0. If I were grading it I'd give you full credit
minus epsilon if the differences were very normal looking, and I'd
take points off for doing ttests if the differences were not
reasonably normal. That's assuming they just asked if there was a
difference. If they asked about a difference in MEANS, you are stuck
with t.

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