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Part IV: Guesstimating and Hypothesizing with Confidence
Not to worry! The percentage to the left (below) a negative t-value is the same
as the percentage to the right (above) the positive t-value, due to symmetry.
So to find the p-value for your negative test statistic, look up the positive
version of your test statistic on the t-table, find the corresponding right tail
(greater-than) probability, and use that.
For example, suppose your test statistic is –2.7105 with 9 degrees of freedom
and H is the less-than alternative. To find your p-value, first look up +2.7105
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on the t-table; by the work in the previous section, you know its p-value falls
between the column headings 0.025 and 0.010. Because the t-distribution is sym-
metric, the p-value for –2.7105 also falls somewhere between 0.025 and 0.010.
Again you reject H because these values are both less than or equal to 0.05.
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Examining the not-equal-to alternative
To find the p-value when your alternative hypothesis (H ) is not-equal-to,
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simply double the probability that you get from the t-table when you look up
your test statistic. Why double it? Because the t-table shows only greater-than
probabilities, which are only half the story. To find the p-value when you have
a not-equal-to alternative, you must add the p-values from the less-than and
greater-than alternatives. Because the t-distribution is symmetric, the less-than
and greater-than probabilities are the same, so just double the one you looked
up on the t-table and you’ll have the p-value for the not-equal-to alternative.
For example, if your test statistic is 2.7171 and H is a not-equal-to alterna-
a
tive, look up 2.7171 on the t-table (df = 9 again), and you find the p-value lies
between 0.025 and 0.010, as shown previously. These are the p-values for the
greater-than alternative. Now double these values to include the less-than
alternative and you find the p-value for your test statistic lies somewhere
between 0.025 ∗ 2 = 0.05 and 0.010 ∗ 2 = 0.020.
Testing One Population Proportion
When the variable is categorical (for example, gender or support/oppose)
and only one population or group is being studied (for example, all registered
voters), you use the hypothesis test in this section to test a claim about the
population proportion. The test looks at the proportion (p) of individuals in
the population who have a certain characteristic — for example, the propor-
tion of people who carry cellphones. The null hypothesis is H : p = p , where
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p is a certain claimed value of the population proportion, p. For example, if
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the claim is that 70% of people carry cellphones, p is 0.70. The alternative
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hypothesis is one of the following: p > p , p < p , or p ≠ p . (See Chapter 14 for
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more on alternative hypotheses.)

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