ST512.
Lab 2 KEY.
1.
Answers will vary.
2.
1.734
3.
Answers will vary.
Observed type I error rate when variances are equal should be
approximately 5%.
Observed type I error rate when variances are not equal should be around 7-
10%.
4.
In this case, unequal variances inflates the Type I error rate of the standard 5% significance
level test.
That is to say, using the standard
t
-test would lead one to reject a true null hypothesis
more than 5%
of the time.
Thus,
p
-values and reject / do not reject decisions are not
trustworthy.
5.
Even when all the assumptions are appropriate, there is an element of randomness in whether
a true null hypothesis is rejected in any single data set, or in any collection of data sets.
Thus, we
wouldn't expect the observed type I error rate to be exactly equal to the significance level, even if
the test is performing as it should. This is a bit like flipping a biased coin.

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