the other group used an assembly line that moved at a fixed pace. After two
weeks, all the workers took a test of job satisfaction. Then they switched work
set-ups and took the test again after two more weeks. The response variable is
the difference in satisfaction scores, self-paced minus machine-paced.
State appropriate hypotheses for performing a significance test.
The parameter of interest is the mean
µ
of the differences (
self-paced
minus
machine-paced
) in job satisfaction scores in the population of all assembly-
line workers at this company.
Because the initial question asked whether job satisfaction differs, the
alternative hypothesis is two-sided; that is, either
µ
< 0 or
µ
> 0. For simplicity,
we write this as
µ
0.
That is:
H
0
:
µ
= 0
H
a
:
µ
0
24
Test Statistic
A test of significance is based on a statistic that estimates the
parameter that appears in the hypotheses. When
H
0
is true, we expect
the estimate to take a value near the parameter value specified in
H
0
.
Values of the estimate far from the parameter value specified by
H
0
give evidence against
H
0
.
A
test statistic
calculated from the sample data measures how far
the data diverge from what we would expect if the null hypothesis
H
0
were true.
Large values of the statistic show that the data are not consistent
with
H
0
.
z
estimate - hypothesized value
standard deviation of the estimate

11/17/2012
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25
P-
Value
The null hypothesis
H
0
states the claim that we are seeking evidence
against
. The probability that measures the strength of the evidence
against a null hypothesis is called a
P
-value
.
The probability, computed assuming
H
0
is true, that the statistic
would take a value as extreme as or more extreme than the one
actually observed is called the
P
-value
of the test. The smaller
the
P
-value, the stronger the evidence against
H
0
provided by
the data.
Small
P
-values are evidence against
H
0
because they say that the
observed result is unlikely to occur when
H
0
is true.
Large
P
-values fail to give convincing evidence against
H
0
because
they say that the observed result is likely to occur by chance when
H
0
is true.
26
Statistical Significance
The final step in performing a significance test is to draw a conclusion
about the competing claims you were testing. We will make one of two
decisions based on the strength of the evidence against the null
hypothesis (and in favor of the alternative hypothesis)
ʊ
reject
H
0
or fail
to reject
H
0
.
If our sample result is too unlikely to have happened by chance
assuming
H
0
is true, then we
䇻
ll reject
H
0
.
Otherwise, we will fail to reject
H
0
.
Note:
A fail-to-reject
H
0
decision in a significance test doesn’t mean
that
H
0
is true. For that reason, you should never
䇾
accept
H
0
䇿
or use
language implying that you believe
H
0
is true.
In a nutshell, our conclusion in a significance test comes down to:
P
-value small
ĺ
reject
H
0
ĺ
conclude
H
a
(in context)
P
-value large
ĺ
fail to reject
H
0
ĺ
cannot conclude
H
a
(in context)