chapter 8 review - weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfchapter 8...
TRANSCRIPT
![Page 1: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/1.jpg)
AP STATISTICS
Chapter 8 Review
![Page 2: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/2.jpg)
8.1 Objectives:ü Distinguish between a statistic and a population characteristicü Understand the definition of a statisticü Understand the definition of sampling variabilityü Understand the definition of a sampling distribution
![Page 3: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/3.jpg)
8.1 Objectives:ü Have a sense that all statistics have sampling distributions
![Page 4: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/4.jpg)
8.2 Objectives:ü Understand the general properties of the sampling distribution of the sample meanü Understand the conditions for applying the Central Limit Theorem
![Page 5: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/5.jpg)
8.2 Objectives:ü Be able to use the Central Limit Theorem and the normal curve probability calculations to find the the probability that the sample mean falls in a given interval when the sample size is large.ü Have a sense the the Central Limit Theorem can be applied if nexceeds 30
![Page 6: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/6.jpg)
8.3 Objectives:ü Understand the general properties of the sampling distribution of the sample proportionü Find the mean and standard deviation of the sampling distribution of given p and the sample size.
![Page 7: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/7.jpg)
8.3 Objectives:ü Be able to use the properties of the sampling distribution of the sample proportion and the normal curve to find the probability that the sample proportion falls in a given interval when the sample size is largeü Have a sense that the Central Limit Theorem is being applied to a rescaled binomial random variable
![Page 8: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/8.jpg)
1998 Form A FR #1
1998 Form A FR #1 Rubric
2010 Form A FR #4b
2010 Form A FR #4b Rubric
![Page 9: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/9.jpg)
Statistic• A number that that can be computed from
sample data
• Some statistics we will use includex – sample means – standard deviationp – sample proportion
• The observed value of the statistic depends on the particular sample selected from the population and it will vary from sample to sample.
![Page 10: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/10.jpg)
Sampling Distributions• The probability distribution of a
statistic: The sampling distribution describes the long-run behavior of the statistic.
![Page 11: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/11.jpg)
Sampling Distributions of X• The probability distribution of the
sample mean X based on a random sample of size n. When the population is normal or the sample size is large, the sampling distribution of X is (approximately) normal.
![Page 12: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/12.jpg)
• The mean of the sampling distribution EQUALS the mean of the population.
• As the sample size increases, the standard deviation of the sampling distribution decreases.
µx = µ
asn σx
![Page 13: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/13.jpg)
General Properties of Sampling Distributions of X
Rule 1:
Rule 2:
This rule is exact if the population is infinite, and is approximately correct if the population is finite and no more than 10% of the population is included in the sample
µµ =x
nxσσ =
![Page 14: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/14.jpg)
General Properties Continued . . .Rule 3:
When the population distribution is normal, the sampling distribution of X is also normal for any sample size n.
![Page 15: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/15.jpg)
General Properties Continued . . .
Rule 4: Central Limit TheoremWhen n is sufficiently large, the sampling distribution of X is well approximated by a normal curve, even when the population distribution is not itself normal.
CLTcansafelybeappliedifn exceeds30.
![Page 16: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/16.jpg)
Sampling Distributions of p• The probability distribution of the
sample proportion p, based on a random sample of size n. When the sample size is sufficiently large, the sampling distribution of p is approximately normal.
![Page 17: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/17.jpg)
General Properties for Sampling Distributions of p
Rule 1:
Rule 2:
pp =µ ˆ
npp
p)1(
ˆ−
=σ
Rule 3: When n is large and p is not too near 0 or 1, the sampling distribution of pis approximately normal.
![Page 18: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/18.jpg)
Chapter 8 Review
Review Questions
![Page 19: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/19.jpg)
Chapter 8 Review
Review Questions
![Page 20: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/20.jpg)
1.AccordingtointernaltestingdonebytheGet-A-Griptirecompany,themeanlifetimeoftiressoldonnewcarsis23,000miles,withastandarddeviationof2500miles.
IftheclaimbyGet-A-Gripistrue,whatisthemeanofthesamplingdistributionof forsamplesofsizen =4?
![Page 21: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/21.jpg)
1.AccordingtointernaltestingdonebytheGet-A-Griptirecompany,themeanlifetimeoftiressoldonnewcarsis23,000miles,withastandarddeviationof2500miles.
IftheclaimbyGet-A-Gripistrue,whatisthestandarddeviationofthesamplingdistributionof forsamplesofsizen =4?
𝜎"# =𝜎"𝑛=25002
= 1250
![Page 22: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/22.jpg)
1.AccordingtointernaltestingdonebytheGet-A-Griptirecompany,themeanlifetimeoftiressoldonnewcarsis23,000miles,withastandarddeviationof2500miles.
Ifthedistributionoftirelifeisapproximatelynormal,whatistheprobabilitythatthemeanofarandomsampleofsizen =4oftirelifetimeswillbelessthan20,000miles?
![Page 23: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/23.jpg)
2.Considersamplingfromapopulationwhoseproportionofsuccessesisp =0.1.Asthesamplesize,n,increases,somecharacteristicsofthesamplingdistributionofp change.Whichofthefollowingcharacteristicswillchangeasn increases,andwhatisthenatureofthechange?
Themeanofthesamplingdistributionof
Asthesamplesizeincreases, staysthesame.
![Page 24: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/24.jpg)
2.Considersamplingfromapopulationwhoseproportionofsuccessesisp =0.1.Asthesamplesize,n,increases,somecharacteristicsofthesamplingdistributionofp change.Whichofthefollowingcharacteristicswillchangeasn increases,andwhatisthenatureofthechange?
Thestandarddeviationofthesamplingdistributionof
Asthesamplesizeincreases,getssmaller.
![Page 25: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/25.jpg)
2.Considersamplingfromapopulationwhoseproportionofsuccessesisp =0.1.Asthesamplesize,n,increases,somecharacteristicsofthesamplingdistributionofp change.Whichofthefollowingcharacteristicswillchangeasn increases,andwhatisthenatureofthechange?
Theshapeofthesamplingdistributionof𝑝+?
Asthesamplesizeincreases,thesamplingdistributionof𝑝+ becomeslessskewedandmorenormal.
![Page 26: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/26.jpg)
3. Supposeweartificiallycategorizepopulationsasapproximatelynormalornot,andsamplesaslargeorsmall.Thiscategorizationresultsin4categories:
a)Smallsamplesfromanapproximatelynormalpopulationb)Largesamplesfromanapproximatelynormalpopulationc)Smallsamplesfromapopulationthatisnotapproximatelynormald)Large samplesfromapopulationthatisnotapproximatelynormal
What,ifanything,canbesaidabouttheshape ofthesamplingdistributionof foreachofthese4situations?
![Page 27: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/27.jpg)
a) Smallsamplesfromanapproximatelynormalpopulation
Thesamplingdistributionof𝑋# willbeapproximatelynormal.
![Page 28: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/28.jpg)
b)Largesamplesfromanapproximatelynormalpopulation
Thesamplingdistributionof𝑋# willbeapproximatelynormal
![Page 29: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/29.jpg)
c)Smallsamplesfromapopulationthatisnotapproximatelynormal
Thesamplingdistributionof𝑋# willresembletheshapeoftheoriginalpopulation(notapproximatelynormal).
![Page 30: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/30.jpg)
d)Largesamplesfromapopulationthatisnotapproximatelynormal
Thesamplingdistributionof𝑋# willbeapproximatelynormal
![Page 31: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/31.jpg)
4.Considersamplingfromaskewed population.Asthesamplesize,n,increases,somecharacteristicsofthesamplingdistributionof change.Doesanincreasingsamplesizecausechangesinthecharacteristicsofthesamplingdistributionshownbelow?Ifso,specificallyhowdoesthesamplingdistributionchange?
Themeanofthesamplingdistributionof
As the sample size increases, stays the same.
![Page 32: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/32.jpg)
4.Considersamplingfromaskewed population.Asthesamplesize,n,increases,somecharacteristicsofthesamplingdistributionof change.Doesanincreasingsamplesizecausechangesinthecharacteristicsofthesamplingdistributionshownbelow?Ifso,specificallyhowdoesthesamplingdistributionchange?
Thestandarddeviationofthesamplingdistributionof
As the sample size increases, gets smaller.
![Page 33: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/33.jpg)
4.Considersamplingfromaskewed population.Asthesamplesize,n,increases,somecharacteristicsofthesamplingdistributionof change.Doesanincreasingsamplesizecausechangesinthecharacteristicsofthesamplingdistributionshownbelow?Ifso,specificallyhowdoesthesamplingdistributionchange?
Thestandarddeviationofthesamplingdistributionof
As the sample size increases, will decrease.
![Page 34: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/34.jpg)
4.Considersamplingfromaskewed population.Asthesamplesize,n,increases,somecharacteristicsofthesamplingdistributionof change.Doesanincreasingsamplesizecausechangesinthecharacteristicsofthesamplingdistributionshownbelow?Ifso,specificallyhowdoesthesamplingdistributionchange?
The shapeofthesamplingdistributionof
Asthesamplesizeincreases,thedistributionof𝑋#becomeslessskewedandmorenormal.
![Page 35: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/35.jpg)
5.Considerthefollowing"population":{2,2,4,5}.Supposethatarandomsampleofsizen =2istobeselectedwithoutreplacement fromthispopulation.Thereare6possiblesamples(sincetheorderofselectiondoesnotmatter).Computethesamplemean foreachofthesesamplesandusethatinformationtoconstructthesamplingdistributionof𝑋# .(Displayitintableform.)
![Page 36: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/36.jpg)
The6possiblesamplesinclude2and2,2and4,2and5,2and4,2and5,4and5.
Thedistributionof 𝑋# is:
𝑋# 2 3 3.5 4.5𝑃 𝑋# 1
626
26
16
![Page 37: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/37.jpg)
6.Somebiologistsbelievetheevolutionofhandednessislinkedtocomplexbehaviorssuchastool-use.Underthistheory,handednesswouldbegeneticallypassedonfromparentstochildren.Thatis,left-handedparentswouldbemorelikelytohaveleft-handedchildrenthanright-handedparents.Analternatetheoryassertsthathandednessshouldberandom,withleft- andright-handednessequallylikely.Inarecentstudyusingasimplerandomsampleofn =76right-handedparents,50ofthechildrenbornwereright-handed.(p =0.658.)Supposehandednessisarandomoccurrencewitheitherhandequallylikelytobedominant,implyingthattheprobabilityofaright-handedoffspringisp =0.50.
![Page 38: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/38.jpg)
Inarecentstudyusingasimplerandomsampleofn =76right-handedparents,50ofthechildrenbornwereright-handed.(p =0.658.)Supposehandednessisarandomoccurrencewitheitherhandequallylikelytobedominant,implyingthattheprobabilityofaright-handedoffspringis p=0.50.
Showthatitisreasonabletoapproximatethesamplingdistributionof usinganormaldistribution.
![Page 39: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/39.jpg)
Inarecentstudyusingasimplerandomsampleofn =76right-handedparents,50ofthechildrenbornwereright-handed.(p =0.658.)Supposehandednessisarandomoccurrencewitheitherhandequallylikelytobedominant,implyingthattheprobabilityofaright-handedoffspringis p=0.50.Assumingleft- andright-handedchildrenareequallylikelyfromright-handedparents,whatistheprobabilityofobservingasampleproportionofatleast𝑝+ =0.658?𝜇0+ = 𝑝 = 0.5
𝜎0+ =𝑝(1 − 𝑝)
𝑛 =0.5(0.5)76 = 0.0574
𝑃 �̂� ≥ .658 = 𝑛𝑜𝑟𝑚𝑎𝑙𝑐𝑑𝑓 .658,∞, . 5,0.0574 = 0.0030
![Page 40: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/40.jpg)
7.Youwillbeaskedtosketchcurvesrepresentingthedistributionsofasetofdata,aswellasthesamplingdistributionsofthemeanunderdifferentconditions.Youneednotgetthesegraphsperfectlycorrect,butshouldclearlyindicatedifferentaspectsofthecurves,suchaslocation,variability,andshape.
TheStateFisheriesDepartmentwishestostocktheStyxRiverwithfish,andwouldlikethespeciestonotonlysurvivebutthrive.(The"substrate"ofariverisanimportantdeterminantofthequalityofspawninghabitat.)Thepebblediametersintheriverareapproximatelynormallydistributedwithameanof24mm,andastandarddeviationof8mm.TheFisheriespeoplewillselectarandomsampleofpebblesfromtheStyxRiverinanattempttojudgetheaveragepebblesize.
![Page 41: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/41.jpg)
Onthescalebelow,sketchcurvesrepresentingthedistributionoftheoriginalpopulationandthesamplingdistributionof𝑋# forasampleofsizen =16.
the mean will remain the same , the shape will remain normal, while the standard deviation will decrease from to , making the graph of 𝑋# skinnier and taller.
![Page 42: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/42.jpg)
Whatistheapproximateprobabilitythatasampleofn =16fromthispopulationwouldresultinasamplemeangreaterthan30mm?
𝜇"# = 𝜇" = 24
𝜎"# =𝜎"𝑛=84
𝑃 𝑋# ≥ .30 = 𝑛𝑜𝑟𝑚𝑎𝑙𝑐𝑑𝑓 30,∞, 24,2 = 0.0013
![Page 43: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/43.jpg)
Anotherissuethatmustbeconsideredinstockingariverwithfishisthatnotonlynaturalpredatorsofthefish,butfishermenandfisherwomen(fisherpersons?)willbetakingfishfromtheriver,andthusdrivingthepopulationdown.ThegraphbelowisarelativefrequencyhistogramofthelengthsofthegentleHecatefishintheStyxRiver,asrecordedduringamassivefishtaggingsurvey.Themeanlengthforthesefishwas0.8feet.
![Page 44: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/44.jpg)
Supposeweweretotakearandomsample,n =4,fromthispopulationoffishandmeasuretheirlengths.Describetheshape,center,andspreadofthesamplingdistributionof.
Theshapeofthedistributionwillbeskewedright,butnotasmuchasthepopulation.Itwillnotbeapproximatelynormalbecausethesamplesizeissmall(n =4).Themeanofthedistributionwillremainthesameasthatofthepopulation,𝜇"# = 𝜇" = 0.8.Thestandarddeviationofthedistribution,𝜎"# =
EFG= EF
H,however,willbehalfofwhatitwasinthe
originalpopulation.
![Page 45: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/45.jpg)
8.Thefirstlarge-scalestudyofthehumansexratioinvolvedover6,000familieseachhaving12children.(Thiswasdonein19thCenturyGermany--largefamiliesweremorecommonthenandthere.)52%ofthechildrentheyobservedwereboys.Supposethat21stCenturyresearcherswishtoreplicatethisobservationalstudy.Inordertoseeifthisproportionofboysmighthavechangedintheinterveningyears,supposetheresearcherstrackdown50familieswith12children.Fromthese600children,arandomsampleof50childrenistaken.30ofthe50childrenwereboys(p =0.6.)
![Page 46: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/46.jpg)
52%ofthechildrentheyobservedwereboys……50familieswith12children.Fromthese600children,arandomsampleof50childrenistaken.30ofthe50childrenwereboys(p =0.6.)Showthatitisreasonabletoapproximatethesamplingdistributionof usinganormaldistribution.
np =50(.52)=26 ≥10andn(1- p)=50(1- .52)=24 ≥10
![Page 47: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/47.jpg)
52%ofthechildrentheyobservedwereboys……50familieswith12children.Fromthese600children,arandomsampleof50childrenistaken.30ofthe50childrenwereboys(p =0.6.)Ifthemoderntruepopulationproportionofnewbornboysisp =0.52,whatistheprobabilityofobservingasampleproportionofatleast=0.6?
𝜇0+ = 𝜇0 = 0.52
𝜎0+ =𝑝(1 − 𝑝)
𝑛 =0.52(0.48)
50 = 0.0707
𝑃 �̂� ≥ .6 = 𝑛𝑜𝑟𝑚𝑎𝑙𝑐𝑑𝑓 .6,∞, . 52,0.0707 = 0.1289
![Page 48: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/48.jpg)
8.32Thenicotinecontentinasinglecigaretteofaparticularbrandhasadistributionwithmean0.8mgandstandarddeviation0.1mg.If100ofthesecigarettesareanalyzed,whatistheprobabilitythattheresultingsamplemeannicotinecontentwillbelessthan0.79?lessthan0.77?X=nicotinecontentofarandomlyselectedcigarette
=averagenicotinecontentof100randomlyselectedcigarettes
𝑋# ≈ 𝑁𝑜𝑟 𝜇"# = 0.8,𝜎"# =0.1100
![Page 49: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/49.jpg)
8.32Thenicotinecontentinasinglecigaretteofaparticularbrandhasadistributionwithmean0.8mgandstandarddeviation0.1mg.If100ofthesecigarettesareanalyzed,whatistheprobabilitythattheresultingsamplemeannicotinecontentwillbelessthan0.79?lessthan0.77?
𝑋# ≈ 𝑁𝑜𝑟 𝜇"# = 0.8,𝜎"# =0.1100
![Page 50: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/50.jpg)
8.32Thenicotinecontentinasinglecigaretteofaparticularbrandhasadistributionwithmean0.8mgandstandarddeviation0.1mg.If100ofthesecigarettesareanalyzed,whatistheprobabilitythattheresultingsamplemeannicotinecontentwillbelessthan0.79?lessthan0.77?
𝑋# ≈ 𝑁𝑜𝑟 𝜇"# = 0.8,𝜎"# =0.1100
![Page 51: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/51.jpg)
8.33Letx1,x2,...,x100 denotetheactualnetweights(inpounds)of100randomlyselectedbagsoffertilizer.Supposethattheweightofarandomlyselectedbaghasadistributionwithmean50poundsandvariance1pound2.Let 𝑋# bethesamplemeanweight(n =100).
a. Describethesamplingdistributionof𝑋#.
=averageweightof100randomlyselectedbagsoffertilizer.
𝑋# ≈ 𝑁𝑜𝑟 𝜇"# = 50,𝜎"# =1100
= 0.1
![Page 52: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/52.jpg)
8.33Letx1,x2,...,x100 denotetheactualnetweights(inpounds)of100randomlyselectedbagsoffertilizer.Supposethattheweightofarandomlyselectedbaghasadistributionwithmean50poundsandvariance1pound2.Let bethesamplemeanweight(n =100).
b.Whatistheprobabilitythatthesamplemeanisbetween49.75poundsand50.25pounds?
![Page 53: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/53.jpg)
8.33Letx1,x2,...,x100 denotetheactualnetweights(inpounds)of100randomlyselectedbagsoffertilizer.Supposethattheweightofarandomlyselectedbaghasadistributionwithmean50poundsandvariance1pound2.Let bethesamplemeanweight(n =100).
c.Whatistheprobabilitythatthesamplemeanislessthan50pounds?
![Page 54: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/54.jpg)
8.34Supposethat20%ofthesubscribersofacabletelevisioncompanywatchtheshoppingchannelatleastonceaweek.Thecablecompanyistryingtodecidewhethertoreplacethischannelwithanewlocalstation.Asurveyof100subscriberswillbeundertaken.Thecablecompanyhasdecidedtokeeptheshoppingchannelifthesampleproportionisgreaterthan.25.Whatistheapproximateprobabilitythatthecablecompanywillkeeptheshoppingchannel,eventhoughtheproportionofallsubscriberswhowatchitisonly.20?
![Page 55: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/55.jpg)
8.34 Whatistheapproximateprobabilitythatthecablecompanywillkeeptheshoppingchannel,eventhoughtheproportionofallsubscriberswhowatchitisonly.20?
�̂�=sampleproportionofsubscriberswhowatch
𝑝+ ≈ 𝑁 𝜇0+ = 0.2, 𝜎0+ =0.2(0.8)100
1 − 𝑃 𝑝+ ≥ 0.25 =
1 − 𝑛𝑜𝑟𝑚𝑎𝑙𝑐𝑑𝑓 0.2,∞, 0.25,0.2(0.8)100
= 0.1056
![Page 56: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/56.jpg)
8.35Waterpermeabilityofconcretecanbemeasuredbylettingwaterflowacrossthesurfaceanddeterminingtheamountlost(ininchesperhour).Supposethatthepermeabilityindexx forarandomlyselectedconcretespecimenofaparticulartypeisnormallydistributedwithmeanvalue1000andstandarddeviation150.
![Page 57: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/57.jpg)
normallydistributedwithmeanvalue1000andstandarddeviation150.a.Howlikelyisitthatasinglerandomlyselectedspecimenwillhaveapermeabilityindexbetween850and1300?
X=Permeabilityindexforarandomlyselectedspecimen
![Page 58: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/58.jpg)
normallydistributedwithmeanvalue1000andstandarddeviation150.b.Ifthepermeabilityindexistobedeterminedforeachspecimeninarandomsampleofsize10,howlikelyisitthatthesamplemeanpermeabilityindexwillbebetween950and1100?𝑋#=averagepermeabilityindexforarandomlyselectedsampleof10specimens
𝑋# ≈ 𝑁𝑜𝑟 𝜇"# = 1000,𝜎"# =15010
= 0.1
![Page 59: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/59.jpg)
normallydistributedwithmeanvalue1000andstandarddeviation150.b.Ifthepermeabilityindexistobedeterminedforeachspecimeninarandomsampleofsize10,howlikelyisitthatthesamplemeanpermeabilityindexwillbebetween850and1300?𝑋#=averagepermeabilityindexforarandomlyselectedsampleof10specimens
𝑋# ≈ 𝑁𝑜𝑟 𝜇"# = 1000,𝜎"# =15010
= 0.1
![Page 60: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/60.jpg)
8.35Waterpermeabilityofconcretecanbemeasuredbylettingwaterflowacrossthesurfaceanddeterminingtheamountlost(ininchesperhour).Supposethatthepermeabilityindexx forarandomlyselectedconcretespecimenofaparticulartypeisnormallydistributedwithmeanvalue1000andstandarddeviation150.a.Howlikelyisitthatasinglerandomlyselectedspecimenwillhaveapermeabilityindexbetween850and1300?b.Ifthepermeabilityindexistobedeterminedforeachspecimeninarandomsampleofsize10,howlikelyisitthatthesamplemeanpermeabilityindexwillbebetween950and1100?between850and1300?
![Page 61: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/61.jpg)
8.36Newsweek(November23,1992)reportedthat40%ofallU.S.employeesparticipatein“self-insurance”healthplans(p =.40).
![Page 62: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/62.jpg)
a.Inarandomsampleof100employees,whatistheapproximateprobabilitythatatleasthalfofthoseinthesampleparticipateinsuchaplan?
=sampleproportionofemployeesintheplan
𝑝+ ≈ 𝑁 𝜇0+ = 0.4, 𝜎0+ =0.4(0.6)100
= 0.0490
![Page 63: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/63.jpg)
b.Supposeyouweretoldthatatleast60ofthe100employeesinasamplefromyourstateparticipatedinsuchaplan.Wouldyouthinkp =.40foryourstate?Explain.
This tells us that, if 40% of people in a state participate in a “self-insurance” plan then it is very unlikely that more than 60 people in a sample of 100 would participate in such a plan. Therefore, if more than 60 people in a sample of 100 were found to participate in this type of plan, we would strongly doubt that for that state.
![Page 64: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/64.jpg)
8.37Theamountofmoneyspentbyacustomeratadiscountstorehasameanof$100andastandarddeviationof$30.Whatistheprobabilitythatarandomlyselectedgroupof50shopperswillspendatotalofmorethan$5300?(Hint:Thetotalwillbemorethan$5300whenthesamplemeanexceedswhatvalue?)X=amountofmoneyspentbyacustomeratadiscountstore
=averageamountofmoneyspentbya50customersatadiscountstore
𝑋# ≈ 𝑁𝑜𝑟 𝜇"# = 100,𝜎"# =3050
= 4.243
![Page 65: Chapter 8 Review - Weeblychristensen60.weebly.com/.../4/54343837/chapter_8_review.pdfChapter 8 Review Review Questions 1. According to internal testing done by the Get - A-Grip tire](https://reader035.vdocuments.site/reader035/viewer/2022081721/5ae7607d7f8b9acc268e930c/html5/thumbnails/65.jpg)
Whatistheprobabilitythatarandomlyselectedgroupof50shopperswillspendatotalofmorethan$5300?
=averageamountofmoneyspentbya50customersatadiscountstore
𝑋# ≈ 𝑁𝑜𝑟 𝜇"# = 100,𝜎"# =3050
= 4.243