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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_hypothesismean2.wasp
Title produced by softwareTesting Mean with known Variance - p-value
Date of computationTue, 11 Nov 2008 12:06:54 -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/t1226430453ncnkkwiye2xyyvl.htm/, Retrieved Sun, 19 May 2024 10:11:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23842, Retrieved Sun, 19 May 2024 10:11:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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 - Critical Value] [Q1 - Critical Value] [2008-11-11 16:59:25] [7dd69dd5bf324136de15cb4f11455bad]
F RMP     [Testing Mean with known Variance - p-value] [Q2 - p-value] [2008-11-11 19:06:54] [e0f4dc76ea1a8276fe566258b977cec4] [Current]
Feedback Forum
2008-11-18 11:17:10 [Steven Hulsmans] [reply] 
Het verschil tussen de sample mean en de null hypothese is niet significant. Er is volgends de p value 41% kans dat we ons vergissen, wat te groot is.
2008-11-20 10:30:57 [Tamara Witters] [reply] 
Hier moet je de eenzijdige toets gebruiken, ( de eenzijdige P-waarde) want we willen slechts in 1 richting meten, nl de kans dat de leverancier meer vet gebruikt dan toegelaten.
De P-waarde bedraagt 41%, d.w.z. indien we de leverancier aanklagen hebben we een kans van 41% dat we ons vergissen. Deze kans is veel te groot! Bijgevolg gaan we de leverancier niet aanklagen we dit zou ons te vel geld kosten.
De verwerpen de nulhypothese niet!
2008-11-20 10:34:56 [Tamara Witters] [reply] 
Je berekening met de R-code is helemaal verkeerd, terwijl in je document wel de juiste oplossing staat...
2008-11-23 10:46:30 [Liese Tormans] [reply] 
Q2:De berekening is helemaal verkeerd, terwijl in je document wel de juiste oplossing staat.

Hier vind je een link met de juiste oplossing
http://www.freestatistics.org/blog/date/2008/Nov/11/t1226411102shadmkmduvu6op3.htm

De student heeft geen conclusie gevormd. De berekeningstabel in het verantwoordingsdocument klopt wel maar die van de link is verkeerd.
De student heeft deze opgave niet opgelost We moeten kijken naar de P-waarde, meer bepaald naar de eenzijdige P-waarde want door naar deze waarde te kijken sluiten we de afwijking naar beneden uit.

We zien dat de p-value 0.41 bedraagt, dit wil zeggen dat we 41% kans hebben dat we ten onrechte een klacht indienen. Dit is een tamelijk groot percentage, dus je kan best geen klacht in te dienen want het risico dat het bedrijf ongegrond een klacht indient is te groot (41 % kans dat je klacht ten onrechte is tegenover 59 % dat ze gegrond is).
2008-11-23 10:48:20 [Liese Tormans] [reply] 
Q3:Ook hier is de berekening (link) helemaal verkeerd, terwijl in je document de juiste oplossing staat.
Hier vind je een link met de juiste oplossing
http://www.freestatistics.org/blog/date/2008/Nov/11/t1226411244pk2f0v16rgwkrrb.htm

Daarnaast is er ook geen conclusie gevormd.

We moeten hier onderzoeken hoe groot de kans is dat we de fraude niet gaan detecteren, dit kan je zien aan de hand van de type II Error waarde. Deze waarde bedraagt +-94%. De kans dat we de leverancier pakken bedraagt dus maar 6%. We kunnen dus concluderen dat de kans zeer klein is.

We hebben 2 mogelijke oplossingen om dit probleem te verhelpen.
De meettechniek verbeteren zodat de type II error verkleind en de pakkans groter wordt.

De steekproef (sample size) vergroten zodat de type II error verkleind en de pakkans vergroot.

Opmerking: De type twee fout kan je enkel detecteren indien je de alternatieve hypothese kent. In dit geval was de alternatieve hypothese 15,2% en de nul hypothese 15%.

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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=23842&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=23842&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23842&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
sample size9
population variance0.36
sample mean5.35
null hypothesis about mean5.2
type I error0.05
Z-value0.749999999999997
p-value (one-tailed)0.226627352376869
p-value (two-tailed)0.453254704753738
conclusion for one-tailed test
Do not reject the null hypothesis.
conclusion for two-tailed test
Do not reject the null hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
sample size & 9 \tabularnewline
population variance & 0.36 \tabularnewline
sample mean & 5.35 \tabularnewline
null hypothesis about mean & 5.2 \tabularnewline
type I error & 0.05 \tabularnewline
Z-value & 0.749999999999997 \tabularnewline
p-value (one-tailed) & 0.226627352376869 \tabularnewline
p-value (two-tailed) & 0.453254704753738 \tabularnewline
conclusion for one-tailed test \tabularnewline
Do not reject the null hypothesis. \tabularnewline
conclusion for two-tailed test \tabularnewline
Do not reject the null hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23842&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]9[/C][/ROW]
[ROW][C]population variance[/C][C]0.36[/C][/ROW]
[ROW][C]sample mean[/C][C]5.35[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]5.2[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]Z-value[/C][C]0.749999999999997[/C][/ROW]
[ROW][C]p-value (one-tailed)[/C][C]0.226627352376869[/C][/ROW]
[ROW][C]p-value (two-tailed)[/C][C]0.453254704753738[/C][/ROW]
[ROW][C]conclusion for one-tailed test[/C][/ROW]
[ROW][C]Do not reject the null hypothesis.[/C][/ROW]
[ROW][C]conclusion for two-tailed test[/C][/ROW]
[ROW][C]Do not reject the null hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23842&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23842&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
sample size9
population variance0.36
sample mean5.35
null hypothesis about mean5.2
type I error0.05
Z-value0.749999999999997
p-value (one-tailed)0.226627352376869
p-value (two-tailed)0.453254704753738
conclusion for one-tailed test
Do not reject the null hypothesis.
conclusion for two-tailed test
Do not reject the null hypothesis


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 9 ; par2 = 0.36 ; par3 = 5.35 ; par4 = 5.2 ; par5 = 0.05 ;
Parameters (R input):
par1 = 9 ; par2 = 0.36 ; par3 = 5.35 ; par4 = 5.2 ; 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))
csn2 <- abs(qnorm(par5/2))
z <- (par3 - par4) / (sqrt(par2/par1))
p <- 1-pnorm(z)
if (par3 == par4)
{
conclusion <- 'Error: the null hypothesis and sample mean must not be equal.'
conclusion2 <- conclusion
} else {
if (p < par5/2)
{
conclusion2 <- 'Reject the null hypothesis'
} else {
conclusion2 <- 'Do not reject the null hypothesis'
}
}
if (p < par5)
{
conclusion <- 'Reject the null hypothesis.'
} else {
conclusion <- 'Do not reject the null hypothesis.'
}
p
conclusion
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,'sample size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'population variance',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'sample mean',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'null hypothesis about mean',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'type I error',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Z-value',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (one-tailed)',header=TRUE)
a<-table.element(a,p)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (two-tailed)',header=TRUE)
a<-table.element(a,p*2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'conclusion for one-tailed test',2,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,conclusion,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'conclusion for two-tailed test',2,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,conclusion2,2)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')