Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_hypothesismean6.wasp

Title produced by software

Testing Sample Mean with known Variance - Confidence Interval

Date of computation

Thu, 13 Nov 2008 03:17:43 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/13/t1226571524gh0lmosjcr8ruz8.htm/, Retrieved Sun, 19 May 2024 11:30:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24548, Retrieved Sun, 19 May 2024 11:30:29 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

156

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...] [2008-11-13 10:17:43] [c4248bbb85fa4e400deddbf50234dcae] [Current]

Feedback Forum

2008-11-15 16:46:13 [Charis Berrevoets] [reply] 
Je gebruikt hier de juiste berekeningsmethode, maar je hebt een foute waarde ingegeven voor de nulhypothese. De vraag is om het betrouwbaarheidsinterval te berekenen voor het echte vetpercentage. Dit was 15,46% en niet 15%. Dit is echter slechts een klein verschil, waardoor de uitkomst ook niet sterk verschillend is.  
Je hebt de 2-zijdige test gebruikt, omdat je 2 grenzen gebruikt. Dit kan natuurlijk, maar hier had je eigenlijk slechts een 1-zijdige test nodig, daar de producent enkel een voordeel zou hebben bij een te hoog percentage (Right one-sided confidence interval at 0.95) en dus zeker niet te weinig vet zou gebruiken.  
De conclusie blijft echter hetzelfde: het vetpercentage ligt binnen het betrouwbaarheidsinterval en is dus niet aan het toeval toe te wijzen. Dit had je nog kunnen vermelden. 
2008-11-18 17:06:00 [72e979bcc364082694890d2eccc1a66f] [reply] 
De student maakt hier gebruik van de 2-sided test. Het is echter de bedoeling om de rechterkant van de 1-sided test te gebruiken omdat enkel een afwijking naar boven kan leiden tot een economisch voordeel. 
Aan deze rechterkant kunnen we dan zien dat de sample mean 15,46% nog binnen het betrouwbaarheisinterval ligt, namelijk 18,9%.
2008-11-20 16:06:14 [Steven Vanhooreweghe] [reply] 
We gebruiken hier het eenzijdig betrouwbaarheidsinterval van de rechterkant want dat is economisch voordelig voor de leverancier (meer vet leveren is goedkoper). De sample mean (0.1546) ligt onder 0.189276559191704 en dus binnen het 95%-betrouwbaarheidsinterval
2008-11-22 20:37:15 [Jessica Alves Pires] [reply] 
Ik ben het eens met de voorgaande opmerkingen. Ik heb er niets aan toe te voegen.

Post a new message

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	'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=24548&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=24548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24548&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Testing Sample Mean with known Variance
Population variance	0.12
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	0.0193357343639964	0.280664265636004
Left one-sided confidence interval at 0.95	0.0403430915365685	+inf
Right one-sided confidence interval at 0.95	-inf	0.259656908463431
more information about confidence interval

\begin{tabular}{lllllllll}
\hline
Testing Sample Mean with known Variance \tabularnewline
Population variance & 0.12 \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 & 0.0193357343639964 & 0.280664265636004 \tabularnewline
Left one-sided confidence interval at  0.95 & 0.0403430915365685 & +inf \tabularnewline
Right one-sided confidence interval at  0.95 & -inf & 0.259656908463431 \tabularnewline
more information about confidence interval \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24548&T=1

[TABLE]
[ROW][C]Testing Sample Mean with known Variance[/C][/ROW]
[ROW][C]Population variance[/C][C]0.12[/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]0.0193357343639964[/C][C]0.280664265636004[/C][/ROW]
[ROW][C]Left one-sided confidence interval at  0.95[/C][C]0.0403430915365685[/C][C]+inf[/C][/ROW]
[ROW][C]Right one-sided confidence interval at  0.95[/C][C]-inf[/C][C]0.259656908463431[/C][/ROW]
[ROW][C]more information about confidence interval[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24548&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	0.12
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	0.0193357343639964	0.280664265636004
Left one-sided confidence interval at 0.95	0.0403430915365685	+inf
Right one-sided confidence interval at 0.95	-inf	0.259656908463431
more information about confidence interval

Parameters (Session):

par1 = 0.12 ; par2 = 27 ; par3 = 0.15 ; par4 = 0.95 ;

Parameters (R input):

par1 = 0.12 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code