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IOE/Stat 265, Fall 2009
Lecture #19:
Hypothesis Tests for One Mean
81
Hypotheses & Test Procedures
82
Tests about a Population Mean
Tests about a Population Proportion
83
84
P  Values
85
Comments on Selection of Tests
1
hort Version of Chapter 8
Short Version of Chapter 8
±
Fundamentally there is no difference between
Interval Estimation (Chapter 7) and Hypothesis
Testing (Chapter 8).
“ ll hypotheses that lie within confidence
±
All hypotheses that lie within confidence
intervals are not rejectable.
All hypotheses that
lie outside confidence intervals are rejectable”.
±
All essential formulas for Chapters 7 and 8 are
2
summarized on following pages.
Overv
iew
81 Overview
I.
Statistical Hypothesis
±
Null and Alternative Hypothesis
yp
±
Test Statistics and Rejection Regions
II.
Errors in Hypothesis Testing
ype I and II errors
±
Type I and II errors
3
Statistical Hypothesis
81 Statistical Hypothesis
tatistical Hypothesis 
laim
bout the value of a
±
Statistical Hypothesis
claim
about the value of a
single population parameter/characteristic (e.g.
mean, variance, proportion), or relationship between
several population characteristics.
±
Examples of Claims:
±
Mean diameter of an engine cylinder is 81 mm.
±
Mean exceeds the mileage standard 30 MPG.
±
Variance is within the standard, 20 microns
2
.
±
% Defective is less than 5%.
±
In hypothesis testing, we collect a
random sample
of data from a population and test the claim.
4
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View Full Documentull and Alternative Hypothesis
Null and Alternative Hypothesis
±
To evaluate a claim, you identify a null and alternative
,y
y
hypothesis.
±
Null Hypothesis, H
0
laim that is initially assumed to be true
±
Claim that is initially assumed to be true.
±
Default Hypothesis (Status Quo)
±
Alternative Hypothesis, H
yp
,
1
±
Assertion that is contradictory to H
0
. (implies the need for change)
±
Null Hypothesis
“is rejected”
if sample evidence suggests
at it is false
If not we
“ ail to reject H ”
that it is false.
If not, we
fail to reject H
0
.
±
So, possible outcomes of test are:
±
Reject H
or
Fail to Reject H
5
0
±
NOTE: failure to reject H
0
is not to say that we have proven H
0
is
true.
xamples: Null Hypotheses (H
Examples:
Null Hypotheses (H
0
)
±
Identify a null and alternative hypothesis
for each of the prior examples.
±
Mean diameter of an engine cylinder is 81 mm.
±
Mean exceeds the mileage standard 30 MPG.
±
Variance is within the standard, 20 microns
2
.
Defective is less than 5%
6
±
% Defective is less than 5%.
“ avored Claim”
Favored Claim
setting up a test we typically have a favored claim
±
In setting up a test, we typically have a favored claim
(default) which is the H
0
.
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 Fall '09
 GaryHerrin

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