Advanced High-School Mathematics

SECTION 6.5 Hypothesis Testing 401

6.5.2 Hypothesis testing of the mean; unknown variance

In this setting, the formulation of the null and alternative hypotheses
don’t change. What changes is the test statistic:

T =

X−μ

Sx

√

n

This has thet-distribution with n−1 degrees of freedom in either of
the two cases itemized on page 386, namely either when we’re sampling
from an approximately normal population or when the sample size is
reasonably large. As in the previous section, the rejection regions at
theαlevel of significance are determined on the basis of the alternative
hypothesis. Furthermore, unless one implements the test automatically
(as on a TI calculator), in finding the boundary of the rejection region
one needs to consider the number of degrees of freedom of thetstatistic.

6.5.3 Hypothesis testing of a proportion

If we encounter the claim that at least 55% percent of the American
voting public prefer candidateAover candidateB, then a reasonable
set of hypotheses to test is