This paper circulates around the core theme of ) A histogram with normality curve is given below for the variable: together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 99. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.
a) Thecontingencytabletodisplaytherelationshipbetween‘Treatmentcode’and‘Timeperiod’to
first infection for patients in this study is given below:
Table 1: Treatment code * Time_period Crosstabulation
Time_period
short time medium time long time Total
Treatment
code
Gamma
Interferon
Count 5 39 32 76
%withinTreatment
code
6.6% 51.3% 42.1% 100.0%
% within Time_period 21.7% 44.8% 53.3% 44.7%
% of Total 2.9% 22.9% 18.8% 44.7%
Placebo Count 18 48 28 94
%withinTreatment
code
19.1% 51.1% 29.8% 100.0%
% within Time_period 78.3% 55.2% 46.7% 55.3%
% of Total 10.6% 28.2% 16.5% 55.3%
Total Count 23 87 60 170
%withinTreatment
code
13.5% 51.2% 35.3% 100.0%
% within Time_period 100.0% 100.0% 100.0% 100.0%
% of Total 13.5% 51.2% 35.3% 100.0%
b) Outofatotalof170patients,5havereceivedGammainterferonandhaveexperienceda
short time to first infection
= 5/170 = 2.9%
c) 28 out of 94 receiving placebo, experience a long time to first infection, which is 29.8%
d) Null hypothesis : There is no association between the two variables
Alternative: There is some association between the two variables
Todisproveindependence,ifitisprovedthatforany2eventsAandB,P(A|B)isnotequalto
P(A) , then A and B are not independent
LetA:NumberofPatientstakingGammaInterferonandBbenumberofpatientsexperiencinga
short time to first infection
P(A|B) =0.217
P(A)=0.447
SinceP(A|B)isnotequaltoP(A),itimpliesthatthereappearstobeanassociation
between‘Treatmentcode’andthe‘Timeperiod’tofirstinfectionofthepatientssufferingfrom
chronic granulotomous disease (cgd )
) A histogram with normality curve is given below for the variable:
b) Fromthehistogramwithnormalcurveoverfitted,thedistributionisclosetonormalasthe
shapeisprettyclosetothebellshape,ifnotperfect.Therearesomeoutlierstowardsthefag
endofthecurveandsomehighvaluesatthestarting,duetowhichthedistributionisnot
perfectly symmetric.
c) The sample size is 170, mean is 84.69 mmHg and Standard dev = 13.019
d) The median is 83 mmHg and IQR is 15
e) Sincethedistributionisfairlynormal,meanisalmostequaltomedian,meanwouldbean
appropriatemeasureofcentraltendencyandstandarddeviation,anappropriatemeasureof
spread, as it is a deviation from the mean
a) The two variables are height and weight and these are continuous variables
b) The scatter plot is :
c) Fromthescatter,itisclearthatthereisalinearpositiverelationshipbetweenthe two
variablesandit isstrong.Thereseemstobenooutliersorleveragepointsinthisscatter
) Thecorrelationcoefficientisusedtomeasurethestrengthanddirection.Thecorrelation
coefficient value is:
Correlations
Height Weight
Height Pearson Correlation 1 .922**
Sig. (2-tailed) .000
N 170 170
Weight Pearson Correlation .922** 1
Sig. (2-tailed) .000
N 170 170
a) The variable is Age and the unit is years
b) Let X be the random variable denoting Age
X~N(14,81)
P(X>25)
ð Standardizing
P(Z>(25-14)/9)
=P(Z>1.222)
=0.111
c) Let x be the age,
P(X
=>P(Z<(x-14)/9) =0.85
a) Thisisanexperimentalstudyasthesubjectsarebeingappliedtotreatmentandthen
observedoveracertainlengthoftime.19subjectsweretreatedtodifferentlevelsofcranberry
juice over the period of three months
b)
i) The response variables are: Antioxidant level , total cholesterol, HDL, and triglycerides
ii) Factoriscranberryjuiceatthreedifferentlevels
iii) The sample size is 19(11 women and 8 men)
c) The 4 principles of experimental design are:
2) Randomize:Therewasrandomizationasthe19subjectsweresplitinto2groupsof
10and9randomly.
3) Replicate: Therearenoreplicateshereasthewholeexperimentwasperformedjust
once
4) Block: Therewerenohomogeneousblocksassigned,justthattherewere2different
randomly assigned groups with different treatments applied.
d) Aconfoundingvariableisonewhichisdirectlyorindirectlyrelatedtotheindependent
variableorthedependentvariable.Aplausibleconfoundingvariablecouldbenumberofhours
ofwalkingduringtheexperimentalstudy.Itisdirectlylinkedtocholesterollevelandthe
resultinglossofcholesterolcanbeconfoundedwithkeepingnumberofhoursofwalkingat
check
Question 6
a) Anappropriatemodelherewould beBinomial.LetXbethenumberofchildrenaged5-17
whoareoverweightorobese.X~Bin(20,0.25),where20isthesamplesizeand0.25isthe
probability of success of the event.
b) The conditions are:
i) The sample size is fixed,n=20
ii) The observations are independent as these are 20 independent 5-17 years old
iii) Eachofthechildiseitherobeseornot
iv) The probability of a child being obese or overweight is 0.25 for each child
c) Mean = 0.25*20 = 5
Variance:0.25*0.75*20=3.75
d) Required probability: P(X>=5)
=1-P(X<=4)
=1- ∑=
−
0 4
20 20 *0.25 *0.75 x to
=1-0.4148
=0.585
e) In this case, X~Bin(100,0.25)
np=25>=10
np(1-p) = 18.75>=10
Sincenpandnp(1-p)>=10,bytheruleofthumb,anormalapproximationtoBinomialis
appropriate here.
Let be the normal counterpart to Binomial X.Then
Y~N(25,18.75)
Required probability: P(X>29.5) (After applying continuity correction)
Standardizing:
P(Z>(29.5-25)/SQRT(18.75)
x x
1) Control: The factors like diet, exercise regime, etc were not controlled in the study
