Page 233 - Statistics for Dummies

Chapter 14: Claims, Tests, and Conclusions
null hypothesis is rejected (that is, there was sufficient evidence against it),
what’s your alternative going to be? Actually, three possibilities exist for the
second (or alternative) hypothesis, denoted H . Here they are, along with
a
their shorthand notations in the context of the pie example:
✓ The population parameter is not equal to the claimed value (H : μ ≠ 5).
✓ The population parameter is greater than the claimed value (H : μ > 5).
✓ The population parameter is less than the claimed value (H : μ < 5).
Which alternative hypothesis you choose in setting up your hypothesis test
depends on what you’re interested in concluding, should you have enough
evidence to refute the null hypothesis (the claim).
For example, if you want to test whether a company is correct in claiming its
pie takes five minutes to make and it doesn’t matter whether the actual aver-
age time is more or less than that, you use the not-equal-to alternative. Your
hypotheses for that test would be H : μ = 5 versus H : μ ≠ 5. a a a 217
o a
If you only want to see whether the time turns out to be greater than what
the company claims (that is, whether the company is falsely advertising its
quick prep time), you use the greater-than alternative, and your two hypoth-
eses are H : μ = 5 versus H : μ > 5.
o a
Finally, say you work for the company marketing the pie, and you think the
pie can be made in less than five minutes (and could be marketed by the
company as such). The less-than alternative is the one you want, and your
two hypotheses would be H : μ = 5 versus H : μ < 5.
o a
How do you know which hypothesis to put in H and which one to put in H ?
o a
Typically, the null hypothesis says that nothing new is happening; the previous
result is the same now as it was before, or the groups have the same average
(their difference is equal to zero). In general, you assume that people’s claims
are true until proven otherwise. So the question becomes: Can you prove
otherwise? In other words, can you show sufficient evidence to reject H ?
o
Gathering Good Evidence (Data)
After you’ve set up the hypotheses, the next step is to collect your evidence
and determine whether your evidence goes against the claim made in H .
o
Remember, the claim is made about the population, but you can’t test the whole
population; the best you can usually do is take a sample. As with any other situ-
ation in which statistics are being collected, the quality of the data is extremely
critical. (See Chapter 3 for ways to spot statistics that have gone wrong.)
Collecting good data starts with selecting a good sample. Two important
issues to consider when selecting your sample are avoiding bias and being

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