Key, Test 3, Spring 2004

Problem 1:
Problem 2: Especially note that on part 5, the student starts with the definition of a type II error: "failing to reject a false null". I think that this is a good way to begin the problem.
Problem 3:
Problem 4: A lot of folks had trouble with the degrees of freedom. It's easy for those who assumed equal variances, but most didn't (those variances look pretty different!). It would have been nice had there been more discussion of the issue. Many folks just launched into the unequal variances formula, leaving me to wonder if they'd actually considered equal variances or not.
You had to come up with your own significance level, since I didn't provide one. This resulted in folks (as here) saying that the result was "statistically significant" but not prescribing a level! That's rather odd, no? I think that some of you relied on the fact that the t-stastistic was quite large to wash out problems of degrees of freedom or alpha, but in that case you need to say so!
Problem 5:
In part 3 this student invokes our standard "less than .001" -- but that was for the particular table that we'd been using in class. In the table I gave you for the test, the smallest p-value is .012, so the remark should have been "less than .012". Actually, since the alternative is two-sided, "less than .024" (twice .012).

And an additional nice solution to part 5:

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