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rwasp_hypothesismean6.wasp

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Testing Sample Mean with known Variance - Confidence Interval

Date of computation

Tue, 11 Nov 2008 08:13:30 -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/11/t12264165048pffucix2tj3o9u.htm/, Retrieved Sun, 19 May 2024 12:18:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23580, Retrieved Sun, 19 May 2024 12:18:05 +0000

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128

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

F       [Testing Sample Mean with known Variance - Confidence Interval] [Q5 Sample Mean ] [2008-11-11 15:13:30] [21d7d81e7693ad6dde5aadefb1046611] [Current]

Feedback Forum

2008-11-21 16:00:01 [90714a39acc78a7b2ecd294ecc6b2864] [reply] 
Je gebruikt 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. De rechter staart is nauwkeuriger, 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 0.1847 en dus binnen het 95%-betrouwbaarheidsinterval. 
2008-11-23 10:43:47 [Jeroen Michel] [reply] 
Hier is je berekening juist. Je geeft tevens ook een volledige conclusie met de juiste argumentatie erin. 
 
Het vetgedrukte gedeelte ‘Right tail’ van de one-sided confidence interval gaan we nemen. Dit aangezien een afwijking naar boven een voordeel (economisch) kan opleveren voor de producent. 
  
De hiervoor genoemde staart is nauwkeuriger aangezien de foutmarge van 5% hieraan wordt toegewezen. Bij de two-sided confidence interval wordt deze verdeeld over de 2 kanten. Hierdoor worden de resultaten extremer. 
  
De sample mean (0.1546) ligt onder 0.189276559191704 en dus binnen het 95%-betrouwbaarheidsinterval. 
2008-11-24 19:49:25 [Ellen Van Ham] [reply] 
We gebruiken hier volgende methode: Testing Population Mean with known Variance - Confidence Interval. 
We kiezen het right-sided confidence interval dat 18,47% bedraagt omdat het gaat om het niet overschrijden van een bepaald vetgehalte. Deze is enkel belangrijk voor ons. 
Als er ook moet nagegaan worden of er niet te weinig vet in het vlees zou mogen zitten, dan zouden we kiezen voor het two-sided confidence interval. Hier moet het vetgehalte binnen het interval liggen. Deze vraag werd correct berekend en beantwoord.

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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	2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23580&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23580&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Testing Sample Mean with known Variance
Population variance	0.012
Sample size	27
Null hypothesis (H0)	0.15
Confidence interval	0.95
Type of Interval	Left tail	Right tail
Two-sided confidence interval at 0.95	0.108680331179696	0.191319668820304
Left one-sided confidence interval at 0.95	0.115323440808296	+inf
Right one-sided confidence interval at 0.95	-inf	0.184676559191704
more information about confidence interval

\begin{tabular}{lllllllll}
\hline
Testing Sample Mean with known Variance \tabularnewline
Population variance & 0.012 \tabularnewline
Sample size & 27 \tabularnewline
Null hypothesis (H0) & 0.15 \tabularnewline
Confidence interval & 0.95 \tabularnewline
Type of Interval & Left tail & Right tail \tabularnewline
Two-sided confidence interval at  0.95 & 0.108680331179696 & 0.191319668820304 \tabularnewline
Left one-sided confidence interval at  0.95 & 0.115323440808296 & +inf \tabularnewline
Right one-sided confidence interval at  0.95 & -inf & 0.184676559191704 \tabularnewline
more information about confidence interval \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23580&T=1

[TABLE]
[ROW][C]Testing Sample 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]Null hypothesis (H0)[/C][C]0.15[/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]0.108680331179696[/C][C]0.191319668820304[/C][/ROW]
[ROW][C]Left one-sided confidence interval at  0.95[/C][C]0.115323440808296[/C][C]+inf[/C][/ROW]
[ROW][C]Right one-sided confidence interval at  0.95[/C][C]-inf[/C][C]0.184676559191704[/C][/ROW]
[ROW][C]more information about confidence interval[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23580&T=1

As an alternative you can also use a QR Code:

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

Testing Sample Mean with known Variance
Population variance	0.012
Sample size	27
Null hypothesis (H0)	0.15
Confidence interval	0.95
Type of Interval	Left tail	Right tail
Two-sided confidence interval at 0.95	0.108680331179696	0.191319668820304
Left one-sided confidence interval at 0.95	0.115323440808296	+inf
Right one-sided confidence interval at 0.95	-inf	0.184676559191704
more information about confidence interval

Parameters (Session):

par1 = 5 ; par2 = 0 ;

Parameters (R input):

par1 = 0.012 ; par2 = 27 ; par3 = 0.15 ; 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 Sample 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,'Null hypothesis (H0)',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#ex6', '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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