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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_babies.wasp
Title produced by softwareExercise 1.13
Date of computationSun, 10 Oct 2010 14:12:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/10/t1286719876i078khsc6w5fxl5.htm/, Retrieved Thu, 02 May 2024 21:59:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=82292, Retrieved Thu, 02 May 2024 21:59:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Exercise 1.13] [Task 2 Babies] [2010-10-10 14:12:08] [214713b86cef2e1efaaf6d85aa84ff3c] [Current]
Feedback Forum
2010-10-16 11:44:29 [abfc2690eac87da053eb0d612ccdbe5b] [reply] 
1) Wanneer je de tijd nog groter had gemaakt (dan 1095 dgn) en bv de keuzemax. van 10 jaar = 3650 dagen had genomen, had je nog een meer accurate oplossing (wet van de grote getallen). Hoe hoger de tijd, hoe meer kans op convergentie. Zo zal je zien dat de lijn bij de grafiek van het grote ziekenhuis nog meer naar een rechte gaat.
2) Dit is enkel een verklaring, geen bewijsvoering . De binomiale verdelingsformule geeft een nauwkeuriger resultaat als de software. Bij de binomiale verdeling geeft de kans weer van een reeks van onafhankelijke resultaten (n=45, groot hospitaal), waarvan elk resultaat een bepaalde waarschijnlijkheid(=p) op succes heeft (p= kans jongen/meisje= 0,5), met een bepaalde succeskans (x=hierbij 60%). En q = 1-p.
p(x) = (n/x)*p^x*q^n-x = 0,9342. Dus de kans dat er op een dag van de 45 geboortes tussen 0 en 27 jongetjes zijn is 0,9342. Daarbij moeten we 1 – de uitkomst doen: 1- 0,9342 = 0,0676 = 6,76%. Nu moeten we weten wat de kans is dat er meer dan 60% jongetjes geboren worden dus 1 - 0,9342 = 0,0676 = 6,76%.

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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=82292&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=82292&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=82292&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)
Number of simulated days1095
Expected number of births in Large Hospital45
Expected number of births in Small Hospital15
Percentage of Male births per day(for which the probability is computed)0.6
#Females births in Large Hospital24691
#Males births in Large Hospital24584
#Female births in Small Hospital8167
#Male births in Small Hospital8258
Probability of more than 60 % of male births in Large Hospital0.0694063926940639
Probability of more than 60 % of male births in Small Hospital0.131506849315068
#Days per Year when more than 60 % of male births occur in Large Hospital25.3333333333333
#Days per Year when more than 60 % of male births occur in Small Hospital48

\begin{tabular}{lllllllll}
\hline
Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.) \tabularnewline
Number of simulated days & 1095 \tabularnewline
Expected number of births in Large Hospital & 45 \tabularnewline
Expected number of births in Small Hospital & 15 \tabularnewline
Percentage of Male births per day(for which the probability is computed) & 0.6 \tabularnewline
#Females births in Large Hospital & 24691 \tabularnewline
#Males births in Large Hospital & 24584 \tabularnewline
#Female births in Small Hospital & 8167 \tabularnewline
#Male births in Small Hospital & 8258 \tabularnewline
Probability of more than 60 % of male births in Large Hospital & 0.0694063926940639 \tabularnewline
Probability of more than 60 % of male births in Small Hospital & 0.131506849315068 \tabularnewline
#Days per Year when more than 60 % of male births occur in Large Hospital & 25.3333333333333 \tabularnewline
#Days per Year when more than 60 % of male births occur in Small Hospital & 48 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=82292&T=1

[TABLE]
[ROW][C]Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)[/C][/ROW]
[ROW][C]Number of simulated days[/C][C]1095[/C][/ROW]
[ROW][C]Expected number of births in Large Hospital[/C][C]45[/C][/ROW]
[ROW][C]Expected number of births in Small Hospital[/C][C]15[/C][/ROW]
[ROW][C]Percentage of Male births per day(for which the probability is computed)[/C][C]0.6[/C][/ROW]
[ROW][C]#Females births in Large Hospital[/C][C]24691[/C][/ROW]
[ROW][C]#Males births in Large Hospital[/C][C]24584[/C][/ROW]
[ROW][C]#Female births in Small Hospital[/C][C]8167[/C][/ROW]
[ROW][C]#Male births in Small Hospital[/C][C]8258[/C][/ROW]
[ROW][C]Probability of more than 60 % of male births in Large Hospital[/C][C]0.0694063926940639[/C][/ROW]
[C]Probability of more than 60 % of male births in Small Hospital[/C][C]0.131506849315068[/C][/ROW]
[ROW][C]#Days per Year when more than 60 % of male births occur in Large Hospital[/C][C]25.3333333333333[/C][/ROW]
[C]#Days per Year when more than 60 % of male births occur in Small Hospital[/C][C]48[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=82292&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=82292&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)
Number of simulated days1095
Expected number of births in Large Hospital45
Expected number of births in Small Hospital15
Percentage of Male births per day(for which the probability is computed)0.6
#Females births in Large Hospital24691
#Males births in Large Hospital24584
#Female births in Small Hospital8167
#Male births in Small Hospital8258
Probability of more than 60 % of male births in Large Hospital0.0694063926940639
Probability of more than 60 % of male births in Small Hospital0.131506849315068
#Days per Year when more than 60 % of male births occur in Large Hospital25.3333333333333
#Days per Year when more than 60 % of male births occur in Small Hospital48


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1095 ; par2 = 45 ; par3 = 15 ; par4 = 0.6 ;
Parameters (R input):
par1 = 1095 ; par2 = 45 ; par3 = 15 ; par4 = 0.6 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
numsuccessbig <- 0
numsuccesssmall <- 0
bighospital <- array(NA,dim=c(par1,par2))
smallhospital <- array(NA,dim=c(par1,par3))
bigprob <- array(NA,dim=par1)
smallprob <- array(NA,dim=par1)
for (i in 1:par1) {
bighospital[i,] <- sample(c('F','M'),par2,replace=TRUE)
if (as.matrix(table(bighospital[i,]))[2] > par4*par2) numsuccessbig = numsuccessbig + 1
bigprob[i] <- numsuccessbig/i
smallhospital[i,] <- sample(c('F','M'),par3,replace=TRUE)
if (as.matrix(table(smallhospital[i,]))[2] > par4*par3) numsuccesssmall = numsuccesssmall + 1
smallprob[i] <- numsuccesssmall/i
}
tbig <- as.matrix(table(bighospital))
tsmall <- as.matrix(table(smallhospital))
tbig
tsmall
numsuccessbig/par1
bigprob[par1]
numsuccesssmall/par1
smallprob[par1]
numsuccessbig/par1*365
bigprob[par1]*365
numsuccesssmall/par1*365
smallprob[par1]*365
bitmap(file='test1.png')
plot(bigprob,col=2,main='Probability in Large Hospital',xlab='#simulated days',ylab='probability')
dev.off()
bitmap(file='test2.png')
plot(smallprob,col=2,main='Probability in Small Hospital',xlab='#simulated days',ylab='probability')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Exercise 1.13 p. 14 (Introduction to Probability, 2nd ed.)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of simulated days',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Expected number of births in Large Hospital',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Expected number of births in Small Hospital',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Percentage of Male births per day
(for which the probability is computed)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Females births in Large Hospital',header=TRUE)
a<-table.element(a,tbig[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Males births in Large Hospital',header=TRUE)
a<-table.element(a,tbig[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Female births in Small Hospital',header=TRUE)
a<-table.element(a,tsmall[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Male births in Small Hospital',header=TRUE)
a<-table.element(a,tsmall[2])
a<-table.row.end(a)
a<-table.row.start(a)
dum1 <- paste('Probability of more than', par4*100, sep=' ')
dum <- paste(dum1, '% of male births in Large Hospital', sep=' ')
a<-table.element(a, dum, header=TRUE)
a<-table.element(a, bigprob[par1])
a<-table.row.end(a)
dum <- paste(dum1, '% of male births in Small Hospital', sep=' ')
a<-table.element(a, dum, header=TRUE)
a<-table.element(a, smallprob[par1])
a<-table.row.end(a)
a<-table.row.start(a)
dum1 <- paste('#Days per Year when more than', par4*100, sep=' ')
dum <- paste(dum1, '% of male births occur in Large Hospital', sep=' ')
a<-table.element(a, dum, header=TRUE)
a<-table.element(a, bigprob[par1]*365)
a<-table.row.end(a)
dum <- paste(dum1, '% of male births occur in Small Hospital', sep=' ')
a<-table.element(a, dum, header=TRUE)
a<-table.element(a, smallprob[par1]*365)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')