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Hypothesis Test Ans.
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You can link to a hypothesis test applet to simulate how decisions
about the null hypothesis vary with the form of the alternative hypothesis and
the level of significance.
- Read Instructions (which include references to topics not yet
covered or reserved for more advanced courses).
- Referring to the top panel, replace the 0.1 level of significance with the
more customary 0.05 level, but otherwise retain all of the default settings.
- Notice that the null hypothesis (mu0) equals 0.0 (mu0 = 0.0), the critical
z equals +/- 1.96, as it should for a two-tailed test (signified in the list
box for H0 as H0:mu=mu0). The relatively small sample size, n, of 5 doesn’t affect the
accuracy of the hypothesis test since the underlying population is known to
be normal.
- Results of each simulation appear as vertical red lines in each of the
three graphs while their numerical counterparts appear below each graph.
- The first graph shows five randomly selected scores as five vertical lines
superimposed over the population distribution; the second panel shows the
one sample mean as a single vertical line superimposed over the sampling
distribution with a horizontal blue bar showing the retention region for the
null hypothesis; the third panel shows two bars for the cumulative
proportion of decisions to retain (0) and reject (1) the null hypothesis.
- Click on "Step" to initiate one simulation. Continue a number of
times until you feel OK about the process. Then, to get 10 simulations in
rapid succession, click on "Run." You can accelerate this process
further by clicking on the "Update Freq" and "Stop Freq"
panels.
Question: After many simulations, does the level of significance
describe the proportion of time that the sample mean actually deviates into the
critical region? How about for a different level of significance? How about for a directional alternative hypothesis?
[Click on list box for H0 to specify the null hypothesis for either a one-tailed
test with an upper critical region (signified as H0:mu<=mu0 in this applet)
or as a one-tailed test with lower critical region (signified as
H0:mu>=mu0).] Answer
There are other simulations in this demonstration that you might wish to
return to after reading subsequent chapters. For example, after reading Chapter
16, you could keep the true population mean equal to zero (mu=0.0),
but step up the value of the hypothesized population mean (mu0 = 0.1, etc.), and note the
cumulative proportion of correct decisions to reject the false null hypothesis.
Or after reading Chapter 18, you could click on sigma "Unknown" and
repeat simulations above for the t test instead of the z test.
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Hypothesis Test