WISE Power Tutorial - Follow-up Questions
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1. Your good friend Bumble found a sample mean of 558 with a sample
of 10000 graduates from Program D. He correctly computed p <.05
and rejected the null
hypothesis that the population mean for Program D is 555. Bumble
concluded that he had strong evidence that the Program D does a very
good job of preparing individuals for the standardized test. Evaluate
Bumble’s conclusion, and interpret his findings. (Hint: Are you
confident that the course produces a substantial increase in test
performance? Why or why not?)
2. Many statisticians argue that hypothesis-testing procedures do not
provide much useful information. Rejecting the null hypothesis tells us
only that it is unlikely that the sample came from a population with a
specific mean. However, procedures like the z-test do not give much
information about the "true" value of the mean from which we are
sampling. Means may be statistically different, but there is no
indication of whether the size of the difference is large enough to be
considered important in real world terms.
How does this relate to results in Question 1 above? (Be sure
to discuss power, effect size, and statistical significance vs.
3. When we reject the null hypothesis, have we always found an
important effect? What other considerations may be important?
4. For several of the sampling exercises we used a one-tailed test
with alpha of .05 (z = 1.645). If we used a two-tailed test with the same
alpha value (z = 1.96), would you have been able to reject your null hypotheses
more or less often? Explain.
5. The Power applet represents a one-tailed hypothesis testing
approach. The applet shows the null and alternative distributions and
the rejection region the area that corresponds to alpha). Using the
applet as a model, draw a graph that represents the rejection regions for a
two-tailed test. Clearly label the area(s) corresponding to rejection of the null hypothesis and the area
in which one would fail to reject the null hypothesis.
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