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Part IV: Guesstimating and Hypothesizing with Confidence

Because the resulting test statistic is negative, it means your sample results
are –1.61 standard errors below (less than) the claimed value for the popula-
tion. How often would you expect to get results like this if H were true? The
chance of being at or beyond (in this case less than) –1.61 is 0.0537. (Keep the
negative with the number and look up –1.61 in the Z-table in the appendix.)
This result is your p-value because H is a less-than hypothesis. (See Chapter 14
a
for more on this.)
Because the p-value is greater than 0.05 (albeit not by much), you don’t have
quite enough evidence for rejecting H . You conclude that the claim that 80%
o
of dentists recommend Cavifree can’t be rejected, according to your data.
However, it’s important to report the actual p-value too, so others can make
their own decisions.
The letter p is used two different ways in this chapter: p-value and p. The
letter p by itself indicates the population proportion, not the p-value. Don’t get
confused. Whenever you report a p-value, be sure you add –value so it’s not
confused with p, the population proportion. o
Comparing Two (Independent)
Population Averages
When the variable is numerical (for example, income, cholesterol level, or
miles per gallon) and two populations or groups are being compared (for
example, men versus women), you use the steps in this section to test a
claim about the difference in their averages. (For example, is the difference
in the population means equal to zero, indicating their means are equal?)
Two independent (totally separate) random samples need to be selected, one
from each population, in order to collect the data needed for this test.
The null hypothesis is that the two population means are the same; in other
words, that their difference is equal to 0. The notation for the null hypothesis
is H : μ = μ , where μ represents the mean of the first population and μ rep-
o 1 2 1 2
resents the mean of the second population.
You can also write the null hypothesis as H : μ – μ = 0, emphasizing the idea
o 1 2
that their difference is equal to zero if the means are the same.
The formula for the test statistic comparing two means (under certain condi-
tions) is:

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