12.1 Power Point

8/7/2019 12.1 Power Point

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Tests About aPopulation Mean

Section 12.1


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Fr at Stats, Again

Remembe r William S. Gosset (1876-1937) f r omGuinness b r ewe ry in Dublin? He became a b r ewe r in1899 and soon became involved in expe r iments andthe statistics needed to unde r stand the data f r om theseexpe r iments.

He was wonde r ing: What a r e the best va r ieties of ba r ley and hops fo r br ewing? How should the y begr own, d r ied, and sto r ed?

The r esults of these field expe r iments va r ied andGosset faced the p r oblem that he didnt know thepopulation standa r d deviation .

He obse r ved that just r eplacing b y s and calling ther esult r oughl y no r mal was not accu r ate enough.

W

W


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The Best Ba r ley

After much wo r k, Gosset developedthe t -dist r ibutions. His new t testidentified the best ba r ley and Guinnesspr omptl y bought up all the availableseeds.

Guinness allowed Gosset to publishhis findings, but not unde r his ownname. He used the name Student, soGossets t test is sometimes called

Students t in his hono r .


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Dete r mining P -values using the t Table

Suppose you a r e testing H 0: = 5versus H a : > 5 based on a sample of sizen = 20 and obtain t = 1.81. Find the P -valueof the test.

Suppose you a r e testing H 0: = 5

versus H a : 5 based on a sample of sizen = 37 and obtain t = -3.17. Find the P -value of the test.


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C omponents of a Significance Test fo r aPopulation Mean (with unknown)

1. Name the procedure: A h ypothesis test fo r a population

mean ( unknown)

2. State the hypotheses and defineany symbols used:

H 0 : = _________ H a : , o r _________


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3 . Check the conditions:

S SRS f r om the population of inte r est I obse r vations a r e independent

(N > 10 n ) N population dist r ibution is ~ N or

the sample size is la r ge enough, o r agr aph of the sample data is ~ N


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4 . Do the math:

C alculate the test statistic and find theassociated p r obabilit y:

Is it alwa ys good to include a sketch

that illust r ates the situation.

0 ( , , | | ) _____ x

t P T or T t s

n

Q! e u u !


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5 . Interpretation in context.

Sa y whethe r you r eject o r fail tor eject the null h ypothesis, linkingyou r statement to the r esults of you r computations.

Explain what you r conclusion meansin the context of the situation.


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Ave r age Bod y Tempe r atu r eB

ody Temperatures(F)Male Female96.9 97.8

97.4 98.097.5 98.297.8 98.297.8 98.2

97.9 98.698.0 98.898.1 98.898.6 99.298.8 99.4

Test the h ypothesisthat the mean of the population f r omwhich the malesample was d r awn

diffe r s f r om 98.6.


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Pai r ed Data o r Not?

Not long afte r the met r ic s ystem was officiall y intr oduced in Aust r alia, a college p r ofesso r asked one g r oup of his students to guess thewidth of thei r lectu r e hall to the nea r est mete r .

He asked a diffe r ent g r oup to guess the width tothe nea r est foot.

If you had to spend time in a hospital, would youwant ca r peting o r a ba r e floo r ? C a r peting wouldr educe noise level and make the atmosphe r emo r e r estful, but ba r e floo r a r e easie r to keepf r ee of ge r ms. 16 r ooms in a Montana hospitalhad thei r ai r measu r ed fo r bacte r ial g r owth.Eight of the r ooms a r e r andoml y ca r peted andthe othe r 8 we r e left ba r e.


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Pa r lez-vous Fr anais ?

The National Endowment fo r theHumanities sponso r s summe r institutes to imp r ove the skills of highschool language teache r s. Oneinstitute hosted 20 Fr ench teache r s fo r fou r weeks. At the beginning of theinstitute, the teache r s took the Mode r nLanguage Associations listening test

of the unde r standing of spokenFr ench. Afte r fou r weeks of imme r sionin Fr ench in and out of class, the y thentook the listening test again. Thefollowing table gives the p r etest andposttest sco r es.


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Teacher Pretest Posttest Posttest-Pretest

1 32 34 2

2 31 31 0

3 29 35 64 10 16 6

5 30 33 3

6 33 36 3

7 22 24 2

8 25 28 3

9 32 26 -6

10 20 26 6

11 30 36 6

12 20 26 6

13 24 27 3

14 24 24 015 31 32 1

16 30 31 1

17 15 15 0

18 32 34 2

19 23 26 3

20 23 26 3


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Did the institute significantl y imp r ove

the teache r s comp r ehension of spoken Fr ench?

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12.1 Power Point