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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_hypothesismean1.wasp
Title produced by softwareTesting Mean with known Variance - Critical Value
Date of computationThu, 13 Nov 2008 15:57:20 -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/13/t12266170896oik62ctrm8dz4u.htm/, Retrieved Mon, 20 May 2024 10:31:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24881, Retrieved Mon, 20 May 2024 10:31:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Kernel Density Estimation] [Bel20 en Downjones] [2008-11-12 17:23:23] [74be16979710d4c4e7c6647856088456]
F RMPD  [Maximum-likelihood Fitting - Normal Distribution] [kelly] [2008-11-12 17:58:06] [74be16979710d4c4e7c6647856088456]
F RMPD      [Testing Mean with known Variance - Critical Value] [Pork quality test Q5] [2008-11-13 22:57:20] [c8dc05b1cdf5010d9a4f2d773adefb82] [Current]
Feedback Forum
2008-11-16 14:33:38 [Julie Govaerts] [reply] 
Gebruikte techniek: Testing Population Mean with known Variance - Confidence Interval

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. 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.
2008-11-17 18:15:48 [Birgit Demulder] [reply] 
We gebruiken inderdaad de 1-tailed test, er kan enkel te veel gebruikt worden. We kijken naar de rechter staart. Enkel een te hoog vetpercentage heeft een economisch voordeel. De sample mean ligt onder de 0,1892 en ligt dus binnen het betrouwbaarheidsinterval. Wanneer we boven deze waarde gaan ligt de sample mean uit dit interval.
2008-11-20 22:08:19 [Toon Wouters] [reply] 
Hier is weer de verkeerde calculator gebruikt. Men had de Testing Population Mean with known Variance – Conidence Interval moeten gebruiken en dan kreeg je deze berekening. http://www.freestatistics.org/blog/date/2008/Nov/11/t1226414217narrdmguclgh08e.htm. Hieruit konden we concluderen : We verkrijgen bij het betrouwbaarheidsinterval van 95% een waarde van 18%, dit is groter dan de 15,46% die eerder werd waargenomen en ligt dus binnen het 95% betrouwbaarheidsinterval. We concluderen hieruit dat er geen fraude gepleegd wordt.
2008-11-24 12:56:06 [Dave Bellekens] [reply] 
Hier had je moeten kiezen voor Testing Population Mean with known Variance - Confidence Interval. We gebruiken hier enkel de right one-sided confidence interval, omdat de leverancier enkel voordeel heeft als hij te veel vet levert. De sample mean ligt onder de 0.1892... en dus valt het binnen het 95% betrouwbaarheids interval.
2008-11-24 21:41:53 [Birgit Van Dyck] [reply] 
de juiste techniek is :Testing Population Mean with known Variance - Confidence Interval. Men moet dan kijken naar de right one-sides confidence interval van de right tail. deze is gelijk aan 0.189276559191704. 0.1546 is kleinder en ligt dus binnen het 95% betrouwbaarheidsinterval.

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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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24881&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24881&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Testing Mean with known Variance
sample size27
population variance0.012
sample mean0.1546
null hypothesis about mean0.15
type I error0.95
critical value (one-tailed)0.184676559191704
confidence interval (two-tailed)(sample mean)[ 0.153278025046460 , 0.155921974953540 ]
conclusion for one-tailed test
Do not reject the null hypothesis.
conclusion for two-tailed test
Reject the null hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
sample size & 27 \tabularnewline
population variance & 0.012 \tabularnewline
sample mean & 0.1546 \tabularnewline
null hypothesis about mean & 0.15 \tabularnewline
type I error & 0.95 \tabularnewline
critical value (one-tailed) & 0.184676559191704 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 0.153278025046460 ,  0.155921974953540 ] \tabularnewline
conclusion for one-tailed test \tabularnewline
Do not reject the null hypothesis. \tabularnewline
conclusion for two-tailed test \tabularnewline
Reject the null hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24881&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]27[/C][/ROW]
[ROW][C]population variance[/C][C]0.012[/C][/ROW]
[ROW][C]sample mean[/C][C]0.1546[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]0.15[/C][/ROW]
[ROW][C]type I error[/C][C]0.95[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]0.184676559191704[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 0.153278025046460 ,  0.155921974953540 ][/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]Reject the null hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24881&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 size27
population variance0.012
sample mean0.1546
null hypothesis about mean0.15
type I error0.95
critical value (one-tailed)0.184676559191704
confidence interval (two-tailed)(sample mean)[ 0.153278025046460 , 0.155921974953540 ]
conclusion for one-tailed test
Do not reject the null hypothesis.
conclusion for two-tailed test
Reject the null hypothesis


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 27 ; par2 = 0.012 ; par3 = 0.1546 ; par4 = 0.15 ; par5 = 0.95 ;
Parameters (R input):
par1 = 27 ; par2 = 0.012 ; par3 = 0.1546 ; par4 = 0.15 ; par5 = 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)
par5<-as.numeric(par5)
c <- 'NA'
csn <- abs(qnorm(par5))
csn2 <- abs(qnorm(par5/2))
if (par3 == par4)
{
conclusion <- 'Error: the null hypothesis and sample mean must not be equal.'
conclusion2 <- conclusion
} else {
cleft <- par3 - csn2 * sqrt(par2) / sqrt(par1)
cright <- par3 + csn2 * sqrt(par2) / sqrt(par1)
c2 <- paste('[',cleft)
c2 <- paste(c2,', ')
c2 <- paste(c2,cright)
c2 <- paste(c2,']')
if ((par4 < cleft) | (par4 > cright))
{
conclusion2 <- 'Reject the null hypothesis'
} else {
conclusion2 <- 'Do not reject the null hypothesis'
}
}
if (par3 > par4)
{
c <- par4 + csn * sqrt(par2) / sqrt(par1)
if (par3 < c)
{
conclusion <- 'Do not reject the null hypothesis.'
} else {
conclusion <- 'Reject the null hypothesis.'
}
}
if (par3 < par4)
{
c <- par4 - csn * sqrt(par2) / sqrt(par1)
if (par3 > c)
{
conclusion <- 'Do not reject the null hypothesis.'
} else {
conclusion <- 'Reject the null hypothesis.'
}
}
c
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,hyperlink('ht_mean_knownvar.htm#overview','critical value (one-tailed)','about the critical value'),header=TRUE)
a<-table.element(a,c)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'confidence interval (two-tailed)
(sample mean)',header=TRUE)
a<-table.element(a,c2)
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')