IntroductionToScientificAnalysis(BIO100)
Name:__________________KEY_____________________
ASSIGNMENT:CHI-SQUARETEST(20POINTS)
Foreachofthefollowingscenarios,youwilltestahypothesisusingthechi-squaretest.Inyour
answers,stateahypothesisandnullhypothesis,reportyourstatisticalresults,andabiological
interpretationofthoseresults.Foralltests,setthesignificancelevel(α)at0.05.
1. (5pts)Undertheproportionalmodel,we
wouldexpectthatbabiesshouldbebornat
thesamefrequencyonallsevendaysofthe
week.Butisthistrue?Table8.1-1liststhe
numberofbabiesbornoneachdayofthe
weekforarandomsampleof350births
from1999.ThedataistakenfromVentura
etal.(2001)andderivedfromtheU.S.
NationalCenterforHealthStatistics,which
recordsinformation,suchastimeanddate
ofbirth,weight,andsex,oneachnewbaby
bornintheU.S.
Day
O
E
(O-E)^2/E
Sunday
33
50
5.78
Monday
41
50
1.62
Tuesday
63
50
3.38
Wednesday
63
50
3.38
Thursday
47
50
0.18
Friday
56
50
0.72
Saturday
47
50
0.18
Total
350
350
X2 15.24
X2critical(df=6)
12.59
Nullhypothesis
Thefrequencyofbabiesbornwillbethesameoneachdayofthe
week.
Alternativehypothesis
Thefrequencyofbabiesbornwilldifferamongdaysoftheweek.
Statisticalresult
Rejectnullhypothesisandacceptalternativehypothesis.
Biologicalconclusion
Thefrequencyofbabiesborndiffersamongdaysoftheweek.
ItappearsthatfewerbirthsoccuronSundaysandmoreduring
themiddleoftheweek.
IntroductionToScientificAnalysis(BIO100)
Name:__________________KEY_____________________
2. (5pts)Inageneticexperimentinvolvingflowercolorinacertainplantspecies,aratioof3:1
blue:whitefloweringplantswasexpected.Theobservedresultswere35blue-floweredplants
and14white-floweredplants.Doestheobservedratioofbluetowhiteflowercolordiffer
significantlyfromtheexpected3:1ratio?
Day
O
E
(O-E)^2/E
Blue-flowered
35
36.75
0.08
White-flowered
14
12.25
0.25
Total
49
49
X2 0.33
2
X critical(df=1)
3.84
Nullhypothesis
Theheterozygouscrosswillresultina3:1phenotypicratioof
blue:whitefloweringplants.
Alternativehypothesis
Theheterozygouscrosswillresultinaphenotypicratioofblue:white
floweringplantsthatdeviatesfroma3:1.
Statisticalresult
Failtorejectthenullhypothesis.
Biologicalconclusion
AspredictedbyMendeliangenetics,theheterozygouscrossresulted
ina3:1phenotypicratioofblue:whitefloweringplants.
Name:__________________KEY_____________________
IntroductionToScientificAnalysis(BIO100)
3. (5pts)Manyparasiteshavemorethanonespeciesofhost.Forsuchparasitestocompletetheir
lifecycles,theymustbeabletogetfromonehosttoanother.Euhaplorchiscaliforniensisisa
parasiteintheTrematoda(parasiticflatworms,orflukes)thatusesthreehostsduringitslife
cycle:shorebirds,hornsnailsandkillfish.Inshorebirds,theparasiticflatwormslayeggsthat
arereleasedinthebird’sfeces.Thehornsnail,Cerithideacalifornica,eatsthefecescontaining
theflatworm’seggs.Insidethesnail,theeggshatch,growtoanotherlife-stage,andcausethe
snailtobecomesterile.Theflatwormlarva(cercariae),whichhasatail-likeappendage,swim
intonearbymarshesandinfectCaliforniakillifish,Fundulusparvipinnis,byattachingtoitsgills.
Onceinfected,thecercariaeworktheirwaytothefish’sbraincase,formacarpet-likelayerover
thebrain,andeventuallyencyst.Whenashorebirdeatsaninfectedkillifish,theparasite
inhabitsthebird’sgutandproduceseggsthatarereleasedinthestoolintothemarshesand
ponds,startingthecycleoveragain.Ithasbeenobservedthatinfectedfishspendmoretime
surfacing,wheretheyaremorevulnerabletobirdpredation.Thisiscertainlytotheworm’s
advantagebecauseitwouldincreaseitschancesofbeingingestedbyashorebirdasitsnext
host.Totestthehypothesisthatinfectionbyflatwormsinfluencestheriskoffishpredationby
birds,LaffertyandMorris(1996)constructedalargeoutdoortankthatwasstockedwiththree
kindsofkillifish:uninfected,lightlyinfected,andhighlyinfected.Thetankwasleftopento
foragingbyshorebirds(e.g.,greategrets,greatblueherons,andsnowyegrets).Belowarethe
numbersoffisheatenaccordingtoparasitelevel.
Observed
Eaten
Noteaten
Total
Expected
Chi-square
Uninfected
1
49
50
Lightly
infected
10
35
45
Highly
infected
37
9
46
Total
48
93
141
Lightly
Highly
Uninfected
infected
infected
17.02
15.32
15.66
32.98
29.68
30.34
50
45
46
Total
48
93
141
Lightly
Highly
Uninfected
infected
infected
Eaten
15.08
1.85
29.08
Noteaten
7.78
0.95
15.01
Total X 2
X2Critical(df=2)
Total
69.76
5.99
Eaten
Noteaten
Total
Name:__________________KEY_____________________
IntroductionToScientificAnalysis(BIO100)
Nullhypothesis
Alternativehypothesis
Statisticalresult
Biologicalconclusion
Infectionofkillfishbyflatwormsisindependent(doesnotaffect)ofthe
riskofkillfishpredationbybirds.
Infectionofkillfishbyflatwormsisdependenton(increases)theriskof
killfishpredationbybirds.
Rejectthenullhypothesis,variablesaredependent.
Killfishinfectedbytheflatwormaremoresusceptibletobirdpredation
thanuninfectedfishbecausetheyspendmoretimesurfacing.
4. (5pts)Usingachi-squaretest,whatcouldwetestusingourclass’heightdata?Presentthe
hypotheses,acontingencytable,conducttheanalysis,andstatetheinterpretations(statistical
andbiological).
Observed
Men
Women
Total
≥170cm
13
6
19
<170
3
26
29
Total
16
32
48
Expected
≥170cm
<170
Total
Chi-square
≥170cm
<170
Total Nullhypothesis
Alternativehypothesis
Statisticalresult
Biologicalconclusion
Women
12.67
19.33
32
Total
19
29
48
Women
3.51
2.30
X 2
X2Critical(df=1)
Total
17.42
3.84
Men
6.33
9.67
16
Men
7.02
4.60
ThereisnoassociationbetweengenderandheightORthereis
nodifferenceinthefrequencyofmenandwomenequaltoor
tallerthan170cm
ThereisanassociationbetweengenderandheightORmoremen
thanwomenareequaltoortallerthan170cm
Rejectthenullhypothesis,variablesareassociated/dependent
Mentendtobetallerthanwomen