Page 247 - Statistics for Dummies

Chapter 15: Commonly Used Hypothesis Tests: Formulas and Examples
the p-value for your test statistic, find which columns correspond to these two
numbers. The number 2.26 appears in the 0.025 column and the number 2.82
appears in the 0.010 column; you now know the p-value for your test
statistic lies between 0.025 and 0.010 (that is, 0.010 < p-value < 0.025).
Using the t-table you don’t know the exact number for the p-value, but because
0.010 and 0.025 are both less than your significance level of 0.05, you reject H ;
you have enough evidence in your sample to say the packages are not being
delivered in 2 days, and in fact the average delivery time is more than 2 days.
The t-table (in the appendix) doesn’t include every possible t-value; just find
the two values closest to yours on either side, look at the columns they’re in,
and report your p-value in relation to theirs. (If your test statistic is greater
than all the t-values in the corresponding row of the t-table, just use the last
one; your p-value will be less than its probability.)

Of course you can use statistical software, if available, to calculate exact
p-values for any test statistic; using software you get 0.012 for the exact o 231
p-value.
Relating t to Z
The next-to-the-last line of the t-table shows the corresponding values from the
standard normal (Z-) distribution for the probabilities listed on the top of each
column. Now choose a column in the table and move down the column look-
ing at the t-values. As the degrees of freedom of the t-distribution increase, the
t-values get closer and closer to that row of the table where the z-values are.
This confirms a result found in Chapter 10: As the sample size (hence
degrees of freedom) increases, the t-distribution becomes more and more
like the Z-distribution, so the p-values from their hypothesis tests are virtu-
ally equal for large sample sizes. And those sample sizes don’t even have to
be that large to see this relationship; for df = 30 the t-values are already very
similar to the z-values shown in the bottom of the table. These results make
sense; the more data you have, the less of a penalty you have to pay. (And of
course, you can use computer technology to calculate more exact p-values
for any t-value you like.)
Handling negative t-values
For a less-than alternative hypothesis (H : xx < xx), your test statistic would
a
be a negative number (to the left of 0 on the t-distribution). In this case, you
want to find the percentage below, or to the left of, your test statistic to get
your p-value. Yet negative test statistics don’t appear on the t-table (in the
appendix).

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