Page 61 - Statistics II for Dummies

Chapter 3: Reviewing Confidence Intervals and Hypothesis Tests
Ho is the model that’s on trial. If you get enough evidence against it, you 45
conclude Ha, which is the model you’re claiming is the right one. If you don’t
get enough evidence against Ho, then you can’t say that your model (Ha) is
the right one.

Gathering your evidence
into a test statistic

A test statistic is the statistic from your sample, standardized so you can look
it up on a table, basically. Although each hypothesis test is a little different,
the main thought is the same. Take your statistic and standardize it in the
appropriate way so you can use the corresponding table for it. Then look
up your test statistic on a table to see where it stands. That table may be
the t-table (Table A-1 in the appendix), the Chi-square table (Table A-3 in the
appendix), or a different table. The type of test you need to use on your data
dictates which table you use.
In the case of testing a hypothesis for a population mean, µ, you use the
sample mean, , as your statistic. To standardize it, you take and convert
it to a value of t by using the formula , where µ is the value in Ho.
0
This value is your test statistic, which you compare to the t-distribution.

Determining strength of evidence
with a p-value

If you want to know whether your data has the brawn to stand up against Ho,
you need to figure out the p-value and compare it to a predetermined cutoff,
α (typically 0.05). The p-value is a measure of the strength of your evidence
against Ho. You calculate the p-value through these steps:

1. Calculate the test statistic (refer to the preceding section for more info
on this).
2. Look up the test statistic on the appropriate table (such as the t-table,
Table A-1 in the appendix).

3. Find the percentage of values on the table that fall beyond your test
statistic. This percentage is the p-value.

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