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SOLUTION:
d. A generic conclusion statement
a.) Under the null hypothesis, . We want to test to see if . Thus:
b.) We will reject if the probability of observing something as or more extreme as 15 out of
60 dropouts ( ) under the assumption of the null hypothesis is less than or equal to
0.05. That is:
( )
c.) We will reject if the observed value of is smaller than some cutoff value of . That
is, it might be the case that would have to be smaller than, say, 13 in order for us to
reject the null hypothesis.
d.) Based on sample evidence, we (choose from below)
a. Reject in favor of
b. Fail to reject . We do not accept as true, but we don‟t have evidence to
conclude otherwise.
As we see from the above example, our hypothesis test needs to have a structured layout. We
need to know ahead of time what we‟ll do.
It is tempting, but we cannot determine our rejection criterion based on what the sample data
tells us! In practice, you can carry this type of philosophy, but you increase the error rate.
Consider, for example, the scenario wherein you take an exam for a biology class. You get the
results back and look at what you missed. You say, “oh, of course I should have put that! I knew
that!” If you told that to the instructor, she may say, “sorry, you didn‟t demonstrate that on the
exam.” Without surprise, we expect this response. Why Because, it is the test that helps to
determine our level of understanding! It is not the other way around. If the instructor allowed
you to change your answer, then the test wouldn‟t really be demonstrating what you knew at that
time of the test. A hypothesis test is quite analogous. We carry one out because we have a hunch.
Always think back to this statement:
If you dig long enough in your data, you will find something!
This, however, looks upon the digging process as a negative thing since it does not justify the
decision questions. In fact, it creates a high likelihood that we are observing a coincidence and
not a solid finding at all! Thus, we increase the probability of error exponentially!
Statistics for Decision-Making in Business © Milos Podmanik Page 217