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8/17/2019 Lab DOE Lecture Note
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Hypothesis Testing
for DierencesBetween Populatio
Means
Lab DOE
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Hypothesis Testing
• The process of decidingstatistically whether thendings of an investigationreect chance or real eects at
a given level of probability.
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Types of Hypothesis Tests
•Tests about a population mean (μ)
• Test about a population variance ()
• Test about a population proportion
• Test for a !ierence between• Population means
• Population proportions
• Population variances
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Tests for !ierences betweepopulation means•
Tests for large samples• Tests for normal populations with "nownvariances
• Test for normal populations with un"nownvariances
• Populations have e#ual variances• Populations have une#ual variances
• Tests for paire! !ata
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Test for !ierences between$ormal Population Means (μ
• %t is more li"ely that in practice we caassume populations are normally!istribute! but !o not "now the popuvariances&
• %n this case an! for sample si'e *+use t statistic in the testing process&
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Main ,ssumptions
•-amples are ta"en ran!omly fromeach population
•The samples from population arein!epen!ent of one another
•.ach population is normally!istribute!
•The population variances are e#u
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.lements of Testing hypothe
• Nll !ypothesis
• "lternative hypothesis
• #dentify level of signicance
• Test statistic
• #dentify re$ection criteria for Nllhypothesis
• %onclsion
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Tests for !ierences betweepopulation means
•,& Hypothesis statements
H*/ 01 2
03
vs&
Ha/ 01 4 03 (two5
si!e!) orHa/ 01 03 (left5si!e!)
or
Ha/ 016 03 (right5
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Testing
-pecifying hypotheses/
!'( )nll* or no eect hypothesis
+,tate-ent of no change or dierence This state-ent is tested directly and either re7ect H
*
or we !o not or fai
to re7ect H*/
!0( research or alternative hypothesis
+The state-ent that must be true if
is re7ecte!/
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Tests for !ierences betweepopulation means•
B& Test statistic
an! !egrees of free!om 2 n1 9 n3 5 3
is the poole! estimate of
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Tests for !ierences betweepopulation means
•:& ;e7ection region
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Tests for !ierences betweepopulation means•
D& :onclusion•%f H* is re7ecte!+ there is a signi<cant statis!ierence between the two population measigni<cance level of
•
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