586
chapter
10
Introduction to Inference
I
Inpt
:Data
0:
60
W:
272
n:
840
P:#Po
ma
'Po
.yi
J
:
,
,
1
1 .
1
1
1
Here are the results of'the z test:
z
=
1.449 and the Pvalue is O.Q7$;6;,
.
'
.
:T
,I:,.
,
,*
i .
If you select "Draw" instead of
calculate^
the
l?ft
dritieal arCa under the normal curve will be
shaded and the zvalue and Pvalue will be digplay'ed.

Po
=275.
z
=I. 44914
P
Value
=.
07365

x
~272.
n
~840.
0
=60.
i3,<,Enter=0x'
J
MAIN
RAD AUTO FUNC
1/1
10.56
CALCULATOR SIGNIFICANCE TESTS
(a)
Use your calculator in this way to find the zvalue and Pvalue for the true value
of the mean
p
in Example 10.14 (575). Check your calculator findings with the num
bers given in Example 10.14.
(b)
If you have data, enter the data into any list and then specify a
z
test. In Example
10.5 (page 546), for example, you would enter the
20
screen tensions into L,/listl.
Then from the Ztest screen, specify "Data" and then enter the appropriate values.
(c) Use your TI83/89 to perform the test of significance described in Exercise 10.39
(page 576).
10.3
MAKING SENSE OF STATISTICAL SIGNIFICANCE
Significance tests are widely used in reporting the results of research in many
fields of applied science and in industry. New pharmaceutical products require
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10.3
Making Sense
of
Statistical Significance.!%?


/
significant evidence of effectiveness and safety. Courts inquire about statistical
significance in hearing class action discrimination cases. Marketers want to
know whether a new ad campaign significantly outperforms the old one, and
medical researchers want to know whether a new therapy performs significant
ly better. In all these uses, statistical significance is valued because it points to
an effect that is unlikely to occur simply by chance.
Carrying out a test of significance is often quite simple, especially if you get
a Pvalue effortlessly from a calculator or computer. Using tests wisely is not so
simple. Here are some points to keep in mind when using or interpreting sig
nificance tests.
Choosing a level of significance
The purpose of a test of significance is to give a clear statement of the degree
of evidence provided by the sample against the null hypothesis. The Pvalue
does this. But sometimes you will make some decision or take some action if
your evidence reaches a certain standard.
A
level of significance
a
sets such a
standard. Perhaps you will publish a research finding if the effect is significant
at the
a
=
0.01 level. Or perhaps your company will lose a lawsuit alleging
racial discrimination if the percent of blacks hired is significantly below the
percent of blacks in the pool of potential employees at the
a
=
0.05 level.
Courts have in fact tended to accept this standard in discrimination cases.1°
Making a decision is different in spirit from testing significance, though
the two are often mixed in practice. Choosing a level
a
in advance makes sense
if you must make a decision, but not if you wish only to describe the strength
of your evidence. Using tests with fixed
a
for decision making is discussed at
greater length in Section 10.4.
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 Fall '08
 O
 Statistical hypothesis testing, Statistical significance, Type I1 error, HO R

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