32 PART III: PROBABILITY AND THE FOUNDATIONS OF INFERENTIAL STATISTICS
CHAPTER SUMMARY ORGANIZED BY LEARNING OBJECTIVE
LO 1: Identify the four steps of hypothesis testing.
• Hypothesis testing, or significance test-
ing, a method of testing a claim or hypothesis
about a parameter in a population, using data
measured in a sample. In this method, we test
some hypothesis by determining the likeli-
hood that a sample statistic could have been
selected, if the hypothesis regarding the popu-
lation parameter were true. The four steps of
hypothesis testing are as follows:
– Step 1: State the hypotheses.
– Step 2: Set the criteria for a decision.
– Step 3: Compute the test statistic.
– Step 4: Make a decision.
LO 2: Define null hypothesis, alternative hypothesis,
level of significance, test statistic, p value, and statisti-
cal significance.
• The null hypothesis (H
0
), stated as the
null, is a statement about a population
parameter, such as the population mean, that
is assumed to be true.
• An alternative hypothesis (H
1
) is a
statement that directly contradicts a null
hypothesis by stating that the actual value of a
population parameter, such as the mean, is
less than, greater than, or not equal to the
value stated in the null hypothesis.
• Level of significance refers to a criterion of
judgment upon which a decision is made
regarding the value stated in a null hypothesis.
• The test statistic is a mathematical formula
that allows researchers to determine the likeli-
hood or probability of obtaining sample out-
comes if the null hypothesis were true. The
value of a test statistic can be used to make
inferences concerning the value of population
parameters stated in the null hypothesis.
• A p value is the probability of obtaining a sam-
ple outcome, given that the value stated in the
null hypothesis is true. The p value of a sample
outcome is compared to the level of significance.
• Significance, or statistical significance,
describes a decision made concerning a value
stated in the null hypothesis. When a null
hypothesis is rejected, a result is significant.
When a null hypothesis is retained, a result is
not significant.
LO 3: Define Type I error and Type II error, and iden-
tify the type of error that researchers control.
• We can decide to retain or reject the null
hypothesis, and this decision can be correct or
incorrect. Two types of errors in hypothesis
testing are called Type I and Type II errors.
• A Type I error is the probability of rejecting
a null hypothesis that is actually true. The
probability of this type of error is determined
by the researcher and stated as the level of sig-
nificance or alpha level for a hypothesis test.
• A Type II error is the probability of retaining
a null hypothesis that is actually false.
LO 4: Calculate the one–independent sample z test
and interpret the results.
• The one–independent sample z test is a
statistical procedure used to test hypotheses
concerning the mean in a single population
with a known variance. The test statistic for
this hypothesis test is
z
M
n
obt
M
M
=
−
=
µ
σ
σ
σ
where
• Critical values, which mark the cutoffs for
the rejection region, can be identified for
any level of significance. The value of the test
statistic is compared to the critical values.
When the value of a test statistic exceeds a
critical value, we reject the null hypothesis;
otherwise, we retain the null hypothesis.
LO 5: Distinguish between a one-tailed and two-
tailed test, and explain why a Type III error is possible
only with one-tailed tests.
• Nondirectional (two-tailed) tests are
hypothesis tests where the alternative hypothe-
sis is stated as not equal to (≠). So we are interested
in any alternative from the null hypothesis.
• Directional (one-tailed) tests are hypoth-
esis tests where the alternative hypothesis is