FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 15:58:54 -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/t1226617168dvzsrtbyyx3cjze.htm/, Retrieved Sun, 19 May 2024 09:22:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24882, Retrieved Sun, 19 May 2024 09:22:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180

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 Q4] [2008-11-13 22:58:54] [c8dc05b1cdf5010d9a4f2d773adefb82] [Current]
Feedback Forum
2008-11-16 14:32:16 [Julie Govaerts] [reply] 
Gebruikte techniek: Testing Mean with known Variance - Sample Size

We moeten onze betafout van 94% reduceren naar veel kleinere betafout van 5% => de pakkans wordt groter. De kans dat we ons vergissen bij het aanvaarden van de nulhypothese (15%) moet dus zeer klein worden, want we willen zeker zijn dat we 15% vet krijgen. Om deze kans zo klein mogelijk te krijgen, zullen we dus zeer veel steekproeven moeten doen
Wanneer we zeker zijn dat we 15% vet krijgen, is er dus zeker geen fraude meer.

We hebben 32466 steekproeven nodig om de betafout op 5% te krijgen. De kosten zouden hier veel te hoog oplopen waardoor het dus onhaalbaar is + te omslachtig = niet realistisch
2008-11-17 17:59:45 [Birgit Demulder] [reply] 
Als we onze type II fout zo fel willen reduceren, dan moeten we een veel te grootte steekproefgrootte gebruiken. Dit is onrealistisch en onhaalbaar. Er zou nog maar weinig vlees in de winkelrekken geraken.
2008-11-20 21:56:56 [Toon Wouters] [reply] 
Hier moest men Testing Mean with known Variance – Sample Size gebruiken. Men kon dan concluderen : Om de type 2 fout te beperken tot 5 % zouden we 32 467 steekroeven moeten nemen, maar dit is niet haalbaar. Dit zou veel geld en tijd kosten.
2008-11-24 12:55:42 [Dave Bellekens] [reply] 
Je had hier gebruik moeten maken van de Testing Mean with known Variance - Sample Size. Je komt dan te weten dat we de steekproef moeten vergroten tot 32466.5 om de pakkans te vergroten tot 95%. Dit is in praktijk echter niet haalbaar, omdat heel tijdrovend en duur is.
2008-11-24 21:38:01 [Birgit Van Dyck] [reply] 
De juiste methode is hier: Testing Mean with known Variance - Sample Size. Men wil dus 95% kans hebben dat men de fraude ontdekt. De type II error is dus 5%, om dit te bekomen moet men de steekproefgrootte verhogen. Door het toenemen van aantal stalen wordt de normaalverdeling smaller en de variantie kleiner. Het resultaat is gigantisch veel stalen. namelijk 32466.5.

Post a new message

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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24882&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24882&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24882&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'George Udny Yule' @ 72.249.76.132






Testing Mean with known Variance
sample size27
population variance0.012
sample mean0.1546
null hypothesis about mean0.152
type I error0.95
critical value (one-tailed)0.186676559191704
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 & 0.152 \tabularnewline
type I error & 0.95 \tabularnewline
critical value (one-tailed) & 0.186676559191704 \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=24882&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]0.152[/C][/ROW]
[ROW][C]type I error[/C][C]0.95[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]0.186676559191704[/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=24882&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24882&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 mean0.152
type I error0.95
critical value (one-tailed)0.186676559191704
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 = 0.152 ; par5 = 0.95 ;
Parameters (R input):
par1 = 27 ; par2 = 0.012 ; par3 = 0.1546 ; par4 = 0.152 ; 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')