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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