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R Software Module

rwasp_hypothesismean5.wasp

Title produced by software

Testing Population Mean with known Variance - Confidence Interval

Date of computation

Wed, 12 Nov 2008 10:05:44 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/12/t1226509586ge01n8ddyu3p3dx.htm/, Retrieved Sun, 19 May 2024 08:44:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24298, Retrieved Sun, 19 May 2024 08:44:52 +0000

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Estimated Impact

171

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F       [Testing Population Mean with known Variance - Confidence Interval] [the pork quality ...] [2008-11-12 17:05:44] [e7b1048c2c3a353441b9143db4404b91] [Current]

Feedback Forum

2008-11-16 14:43:54 [Julie Govaerts] [reply] 
We gebruiken de one-sided confidence interval van de right-tail, omdat enkel de afwijking van het vetpercentage naar boven toe een economisch voordeel voor de producent kan betekenen en omdat we een vermoeden van fraude hebben = rechtszijdig interval. Hij zou eventueel enkel slecht vlees leveren met te veel vet, ipv heel goed vlees met weinig vet. 
De rechter staart is het nauwkeurigst, omdat de volledige 5% (foutmarge) toegewezen wordt aan de rechterkant. (bij de two-sided confidence interval wordt de 5% verdeeld over zowel de linkse als de rechtse staart, wat de resultaten van de two-sided extremer maakt) 
 
De sample mean (0.1546) ligt onder 0.189276559191704 en dus binnen het 95%-betrouwbaarheidsinterval. 
2008-11-20 12:55:32 [Jolien Van Landeghem] [reply] 
Ik sluit mij volledig aan bij de conclusie van Julie. 
2008-11-20 13:37:14 [Jasmine Hendrikx] [reply] 
Eigen evaluatie: 
Er is een juiste berekening gemaakt. Er wordt ook gebruik gemaakt van het right one-sided confidence interval at 0.95.  Dit is correct, maar er wordt hiervoor geen argumentatie gegeven. Een verklaring hiervoor is dat we een vermoeden hebben van fraude (dus te veel vet leveren, want alleen hierbij heeft de leverancier een economisch voordeel). We kijken dus naar de afwijking naar boven. Aanvullend zou er in de bespreking ook nog kunnen vermeld worden dat het steekproefgemiddelde (15.46%) onder de 18.93% (bovengrens van het rechter 95% betrouwbaarheidsinterval)ligt en bijgevolg binnen het betrouwbaarheidsinterval ligt. 
Zoals in de vorige evaluaties ook al vermeld werd, is de rechterstaart nauwkeuriger bij het rechter 95% betrouwbaarheidsinterval ten opzichte van het tweezijdige betrouwbaarheidsinterval, aangezien de volledige foutmarge van 5% toegewezen wordt aan de rechterkant. Bij het tweezijdige betrouwbaarheidsinterval wordt deze 5% verdeeld over zowel de linkse als de rechtse staart, waardoor de grenzen van het tweezijdige betrouwbaarheidsinterval extremer worden. 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24298&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]1 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=24298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24298&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Testing Population Mean with known Variance
Population variance	0.012
Sample size	27
Sample mean	0.1546
Confidence interval	0.95
Type of Interval	Left tail	Right tail
Two-sided confidence interval at 0.95	0.113280331179696	0.195919668820304
Left one-sided confidence interval at 0.95	0.119923440808296	+inf
Right one-sided confidence interval at 0.95	-inf	0.189276559191704
more information about confidence interval

\begin{tabular}{lllllllll}
\hline
Testing Population Mean with known Variance \tabularnewline
Population variance & 0.012 \tabularnewline
Sample size & 27 \tabularnewline
Sample mean & 0.1546 \tabularnewline
Confidence interval & 0.95 \tabularnewline
Type of Interval & Left tail & Right tail \tabularnewline
Two-sided confidence interval at  0.95 & 0.113280331179696 & 0.195919668820304 \tabularnewline
Left one-sided confidence interval at  0.95 & 0.119923440808296 & +inf \tabularnewline
Right one-sided confidence interval at  0.95 & -inf & 0.189276559191704 \tabularnewline
more information about confidence interval \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24298&T=1

[TABLE]
[ROW][C]Testing Population Mean with known Variance[/C][/ROW]
[ROW][C]Population variance[/C][C]0.012[/C][/ROW]
[ROW][C]Sample size[/C][C]27[/C][/ROW]
[ROW][C]Sample mean[/C][C]0.1546[/C][/ROW]
[ROW][C]Confidence interval[/C][C]0.95[/C][/ROW]
[ROW][C]Type of Interval[/C][C]Left tail[/C][C]Right tail[/C][/ROW]
[ROW][C]Two-sided confidence interval at  0.95[/C][C]0.113280331179696[/C][C]0.195919668820304[/C][/ROW]
[ROW][C]Left one-sided confidence interval at  0.95[/C][C]0.119923440808296[/C][C]+inf[/C][/ROW]
[ROW][C]Right one-sided confidence interval at  0.95[/C][C]-inf[/C][C]0.189276559191704[/C][/ROW]
[ROW][C]more information about confidence interval[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24298&T=1

As an alternative you can also use a QR Code:

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

Testing Population Mean with known Variance
Population variance	0.012
Sample size	27
Sample mean	0.1546
Confidence interval	0.95
Type of Interval	Left tail	Right tail
Two-sided confidence interval at 0.95	0.113280331179696	0.195919668820304
Left one-sided confidence interval at 0.95	0.119923440808296	+inf
Right one-sided confidence interval at 0.95	-inf	0.189276559191704
more information about confidence interval

Parameters (Session):

par1 = 0.012 ; par2 = 27 ; par3 = 0.1546 ; par4 = 0.95 ;

Parameters (R input):

par1 = 0.012 ; par2 = 27 ; par3 = 0.1546 ; par4 = 0.95 ;

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)
sigma <- sqrt(par1)
sqrtn <- sqrt(par2)
ua <- par3 - abs(qnorm((1-par4)/2))* sigma / sqrtn
ub <- par3 + abs(qnorm((1-par4)/2))* sigma / sqrtn
ua
ub
ul <- par3 - qnorm(par4) * sigma / sqrtn
ul
ur <- par3 + qnorm(par4) * sigma / sqrtn
ur
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm','Testing Population Mean with known Variance','learn more about Statistical Hypothesis Testing about the Mean when the Variance is known'),3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population variance',header=TRUE)
a<-table.element(a,par1,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample size',header=TRUE)
a<-table.element(a,par2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample mean',header=TRUE)
a<-table.element(a,par3,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence interval',header=TRUE)
a<-table.element(a,par4,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Type of Interval',header=TRUE)
a<-table.element(a,'Left tail',header=TRUE)
a<-table.element(a,'Right tail',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('Two-sided confidence interval at ',par4), header=TRUE)
a<-table.element(a,ua)
a<-table.element(a,ub)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('Left one-sided confidence interval at ',par4), header=TRUE)
a<-table.element(a,ul)
a<-table.element(a,'+inf')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('Right one-sided confidence interval at ',par4), header=TRUE)
a<-table.element(a,'-inf')
a<-table.element(a,ur)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, hyperlink('ht_mean_knownvar.htm#ex5', 'more information about confidence interval','example'),3,TRUE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')

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