----- 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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