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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_hypothesismean4.wasp
Title produced by softwareTesting Mean with known Variance - Sample Size
Date of computationTue, 11 Nov 2008 12:41:24 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/11/t1226432536nh7qa54qi5qyyw2.htm/, Retrieved Mon, 20 May 2024 09:18:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23890, Retrieved Mon, 20 May 2024 09:18:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Testing Mean with known Variance - Type II Error] [marlies.polfliet_...] [2008-11-11 19:24:55] [fdc296cbeb5d8064cb0dbd634c3fdc55]
F RMP     [Testing Mean with known Variance - Sample Size] [marlies.polfliet_...] [2008-11-11 19:41:24] [e221948dd14811c7d88a6530ac2a8702] [Current]
Feedback Forum
2008-11-17 20:06:58 [Stefan Temmerman] [reply] 
De student zegt niets verkeerd, maar hier moet gekeken worden naar de steekproefgrootte.
Hier wil je een type II error hebben van maar 5%. Dit betekent dat je 95% kans wil hebben om de fraude te ontdekken. Dit wordt bereikt door een grotere steekproef te nemen, namelijk één met ruim 32450 metingen. Dit is een bijna onmogelijk werk.
2008-11-19 13:57:10 [7bf28d4d60530086dbc44ae6b648927e] [reply] 
Om de type II te brengen ôp 5 % moet je de steekproefgrootte verhogen. Hoeveel dit moet zijn kan men aflezen bij sample size. hier is dat 32466.5. Dit is dus zeer veel. Het zal dus veel geld en tijd kosten om deze uit te voeren en de controleren.
2008-11-20 16:50:10 [6066575aa30c0611e452e930b1dff53d] [reply] 
Men is vergeten de variantie en de steekproefgrootte te vermelden. Om de proef nauwkeuriger te maken, gaan we de variantie verkleinen. Doordat de variantie verkleint, wordt de normaalverdeling smaller. Een praktisch probleem is dat de steekproefgrootte dan 32 466 bedraagt, dit is een enorm grote steekproef die praktisch niet haalbaar is.
2008-11-22 09:54:58 [Roel Geudens] [reply] 
Verkleinen van de varianti gaat altijd gepaard met een vergroten van de steekproef. Hier wordt de steekproef zodanig groot dat het onmogelijk is om ze uit te voeren.
2008-11-24 18:13:33 [94a54c888ac7f7d6874c3108eb0e1808] [reply] 
De student is vergeten de variantie en de steekproefgrootte te gebruiken. Om de proef nog nauwkeuriger te maken, verkleinen we de variantie. Doordat de variantie verkleint, wordt de normaalverdeling smaller. Een steekproef van 32467 is niet realistisch. Het zou enorm veel tijd en geld kosten.
2008-11-24 20:12:11 [Birgit Van Dyck] [reply] 
Men wil dus 95% kans hebben dat men de fraude ontdenkt. De type II error is dus 5%, om dit te bekomen met met de steekproefgrootte te verhogen. Door het toenemen van het aantal stalen wordt de normaalverdeling smaller en de variantie kleiner. Het resultaat is gigantisch veel stalen. namelijk 32466.5. Waardoor het onderzoek dus zeer omslachtig en duur wordt.

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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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23890&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23890&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Testing Mean with known Variance
population variance0.012
null hypothesis about mean0.15
alternative hypothesis about mean0.152
type I error0.95
type II error0.05
sample size32466.5214491449

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
population variance & 0.012 \tabularnewline
null hypothesis about mean & 0.15 \tabularnewline
alternative hypothesis about mean & 0.152 \tabularnewline
type I error & 0.95 \tabularnewline
type II error & 0.05 \tabularnewline
sample size & 32466.5214491449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23890&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]population variance[/C][C]0.012[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]0.15[/C][/ROW]
[ROW][C]alternative hypothesis about mean[/C][C]0.152[/C][/ROW]
[ROW][C]type I error[/C][C]0.95[/C][/ROW]
[ROW][C]type II error[/C][C]0.05[/C][/ROW]
[ROW][C]sample size[/C][C]32466.5214491449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23890&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:

Testing Mean with known Variance
population variance0.012
null hypothesis about mean0.15
alternative hypothesis about mean0.152
type I error0.95
type II error0.05
sample size32466.5214491449


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.012 ; par2 = 0.15 ; par3 = 0.152 ; par4 = 0.95 ; par5 = 0.05 ;
Parameters (R input):
par1 = 0.012 ; par2 = 0.15 ; par3 = 0.152 ; par4 = 0.95 ; par5 = 0.05 ;
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)
par5<-as.numeric(par5)
c <- 'NA'
csn <- abs(qnorm(par5))
if (par2 == par3)
{
conclusion <- 'Error: the null hypothesis and alternative hypothesis must not be equal.'
}
ua <- abs(qnorm(par4))
ub <- qnorm(par5)
c <- (par2+ua/ub*(-par3))/(1-(ua/ub))
sqrtn <- ua*sqrt(par1)/(c - par2)
samplesize <- sqrtn * sqrtn
ua
ub
c
sqrtn
samplesize
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm','Testing Mean with known Variance','learn more about Statistical Hypothesis Testing about the Mean when the Variance is known'),2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'population variance',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'null hypothesis about mean',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alternative hypothesis about mean',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'type I error',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'type II error',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm#ex4','sample size','example'),header=TRUE)
a<-table.element(a,samplesize)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')