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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_hypothesismean6.wasp
Title produced by softwareTesting Sample Mean with known Variance - Confidence Interval
Date of computationWed, 12 Nov 2008 06:22:58 -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/12/t12264965510bku7u7kfdgxwa5.htm/, Retrieved Sun, 19 May 2024 10:51:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24172, Retrieved Sun, 19 May 2024 10:51:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

Tree of Dependent Computations

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] [Pork quality test...] [2008-11-12 13:22:58] [98255691c21504803b38711776845ae0] [Current]
F RMPD    [Bivariate Kernel Density Estimation] [Various EDA topics] [2008-11-13 10:35:46] [5387335d8669ad018e3e2def51162329]
F RMPD    [Bivariate Kernel Density Estimation] [Various EDA topics] [2008-11-13 14:51:11] [5387335d8669ad018e3e2def51162329]
F RMPD    [Bivariate Kernel Density Estimation] [Various EDA topics] [2008-11-13 14:53:38] [5387335d8669ad018e3e2def51162329]
F RMPD    [Partial Correlation] [Various EDA topics] [2008-11-13 14:58:24] [5387335d8669ad018e3e2def51162329]
F RMPD    [Trivariate Scatterplots] [Various EDA topics] [2008-11-13 15:03:35] [5387335d8669ad018e3e2def51162329]
F RMPD    [Hierarchical Clustering] [Various EDA topics] [2008-11-13 15:25:09] [5387335d8669ad018e3e2def51162329]
F RMPD    [Box-Cox Linearity Plot] [Various EDA topics] [2008-11-13 15:55:58] [5387335d8669ad018e3e2def51162329]
Feedback Forum
2008-11-14 16:13:14 [407693b66d7f2e0b350979005057872d] [reply] 
Deze vraag wordt op exact dezelfde manier opgelost als de vijfde vraag, we volgen hier dezelfde redenering.
We gebruiken voor deze vaag op te lossen dezelfde werkwijze als in vraag 5. Ook hier is de rechter staart is nauwkeuriger, omdat de volledige 5% (foutmarge) toegewezen wordt aan de rechterkant.
(bij de two-sided wordt de 5% verdeeld over de linkse en rechtse tail, wat maakt dat de resultaten voor de two-sided extremer zijn.)
Ook als de nulhypothese hier wordt verhoogd dan nog ligt de sample mean van 0.1546 lager dan de 0.186676559191704dus binnezn het betrouwbaarheidinterval van 95%.


http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/14/t1226667421wbb2si8r9pzvrlj.htm
2008-11-16 18:44:55 [006ad2c49b6a7c2ad6ab685cfc1dae56] [reply] 
Er kan alleen een afwijking naar boven zijn dus moet je een rechtszijdig interval gebruiken (1-sided).
2008-11-24 13:36:06 [Dave Bellekens] [reply] 
Ook hier gebruiken we de one-sided confidence interval van de right tail.

We veranderen hier de 0-hypothese naar 15.2%, maar dan nog ligt de sample mean van de steekproef binnen het 95% betrouwbaarheidsinterval.
2008-11-24 19:07:20 [Kevin Vermeiren] [reply] 
De student heeft de juiste gegevens berekend maar de interpretatie ontbreekt. Net zoals in Q5 diende men het onderzoek te verrichten aan de hand van de “Right one-sided confidence interval at 0.95” naar de rechtse staart omdat we uit gaan fraude. Dus omdat de producent enkel voordeel kan halen uit een situatie waarin er teveel vet verwerkt werd in het vlees. Deze methode is nauwkeuriger omdat de rechtse staart de 5% foutmarge bevat. Dit integenstelling tot het 2-zijdig betrouwbaarheidsinterval want hier wordt de 5% foutmarge toe geschreven aan zowel de linker als de rechter staart. Ook belangrijk is dat men vermeld dat de nul hypothese hier wordt aangepast (nu 15.2%). Deze ingreep verandert echter niets aan het resultaat namelijk, de het steekproefgemiddelde blijft gelegen binnen het 95% betrouwbaarheidsinterval (0.1546< 0.186677). We kunnen dus concluderen dat de sample mean consistent is met het vetproductie percentage.

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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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24172&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24172&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24172&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Testing Sample Mean with known Variance
Population variance0.012
Sample size27
Null hypothesis (H0)0.152
Confidence interval0.95
Type of IntervalLeft tailRight tail
Two-sided confidence interval at 0.950.1106803311796960.193319668820304
Left one-sided confidence interval at 0.950.117323440808296+inf
Right one-sided confidence interval at 0.95-inf0.186676559191704
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) & 0.152 \tabularnewline
Confidence interval & 0.95 \tabularnewline
Type of Interval & Left tail & Right tail \tabularnewline
Two-sided confidence interval at  0.95 & 0.110680331179696 & 0.193319668820304 \tabularnewline
Left one-sided confidence interval at  0.95 & 0.117323440808296 & +inf \tabularnewline
Right one-sided confidence interval at  0.95 & -inf & 0.186676559191704 \tabularnewline
more information about confidence interval \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24172&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]0.152[/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]0.110680331179696[/C][C]0.193319668820304[/C][/ROW]
[ROW][C]Left one-sided confidence interval at  0.95[/C][C]0.117323440808296[/C][C]+inf[/C][/ROW]
[ROW][C]Right one-sided confidence interval at  0.95[/C][C]-inf[/C][C]0.186676559191704[/C][/ROW]
[ROW][C]more information about confidence interval[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24172&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24172&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 Sample Mean with known Variance
Population variance0.012
Sample size27
Null hypothesis (H0)0.152
Confidence interval0.95
Type of IntervalLeft tailRight tail
Two-sided confidence interval at 0.950.1106803311796960.193319668820304
Left one-sided confidence interval at 0.950.117323440808296+inf
Right one-sided confidence interval at 0.95-inf0.186676559191704
more information about confidence interval


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.012 ; par2 = 27 ; par3 = 0.152 ; par4 = 0.95 ;
Parameters (R input):
par1 = 0.012 ; par2 = 27 ; par3 = 0.152 ; 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')