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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_hypothesismean1.wasp
Title produced by softwareTesting Mean with known Variance - Critical Value
Date of computationFri, 07 Nov 2008 05:34:32 -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/07/t1226061338tqybcs5mqsm6p5v.htm/, Retrieved Sun, 19 May 2024 07:10:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22480, Retrieved Sun, 19 May 2024 07:10:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Testing Mean with known Variance - Critical Value] [q1] [2008-11-07 12:34:32] [7596afe9a05f2a2719ece78b1b0e12e6] [Current]
Feedback Forum
2008-11-17 10:21:30 [Nicolaj Wuyts] [reply] 
De cijfergegevens die ingevoerd werden voor het vinden van de mediaan zijn niet geheel correct. De variantie in populatie is 0,012 in plaats van 1,2; de mediaan van de testen moet 0,1546 zijn en de nulhypothese moet 0,15 zijn. Bij het invullen van deze gegevens bekom je een kritische waarde van 0.184676559191704. Je krijgt ook een interval gaan van 0.113280331179696 tot 0.195919668820304. Aangezien onze kritische waarde hier tussen zit, kunnen we aan nemen dat we geen klacht kunnen indienen voor het verhoogde vetgehalte. Men moet ook naar de two-tailed hypothese kijken omdat het vlees dat geleverd wordt door de leverancier, zowel te veel als te weinig vet kan bevatten. Als we kijken naar het advies bij de two-tailed hypothese, staat er: verwerp de nulhypothese niet. Dit wil dus zeggen dat er aan de normen is voldaan qua vetgehalte.
2008-11-17 14:06:55 [Stef Vermeiren] [reply] 
De inputgegevens werden fout ingevoerd (wat blijkbaar een vaak voorkomende fout is.)

nulhypothese: het vetgehalte bevindt zich tussen de grenzen van 13.8% en 16.2%.
alternatieve hypothese: het vetgehalte valt buiten deze twee grenzen.
Type 1-error: de leverancier straffen wanneer hij onschuldig is en dus het vetgehalte in zijn worsten binnen de aangegeven grenzen hield.
We passen hier een 2-sided test toe omdat het vetgehalte binnen de grenzen valt van 13.8% en 16.2% (het vetgehalte moet immers een variantie van 1.2% op 15% hebben).
De type 1-error zegt dat de maximumwaarde gelijk is aan 0.05. Het is dus niet fout wanneer we alfa gelijkstellen aan 0.05. We dienen geen klacht in.
2008-11-24 16:14:05 [4679c4d03f1d346a85e79d87ba60ec2b] [reply] 
Verkeerde invoering van de gegevens. De population variance zou ingevoerd moeten worden als 0.012, bij sample mean zou dit 0.1546 en de nulhypothese zou ingevoerd moeten worden als 0.15. Hierdoor kom je ook een andere critical value uit. Deze zou 0.184676559191704 moeten zijn. De critical value is groter dan de sample mean van 0.1546. Je kan dus zeggen dat we de nulhypothese niet verwerpen en dit toeval is. Omdat het toeval is moet je hier geen klacht indienen. Er zou een one-sided test gebruikt moeten worden om de afwijkingen naar boven te meten.

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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=22480&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=22480&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22480&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 Mean with known Variance
sample size27
population variance1.2
sample mean15.46
null hypothesis about mean15
type I error0.05
critical value (one-tailed)15.3467655919170
confidence interval (two-tailed)(sample mean)[ 15.0468033117970 , 15.8731966882030 ]
conclusion for one-tailed test
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 & 1.2 \tabularnewline
sample mean & 15.46 \tabularnewline
null hypothesis about mean & 15 \tabularnewline
type I error & 0.05 \tabularnewline
critical value (one-tailed) & 15.3467655919170 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 15.0468033117970 ,  15.8731966882030 ] \tabularnewline
conclusion for one-tailed test \tabularnewline
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=22480&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]1.2[/C][/ROW]
[ROW][C]sample mean[/C][C]15.46[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]15[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]15.3467655919170[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 15.0468033117970 ,  15.8731966882030 ][/C][/ROW]
[ROW][C]conclusion for one-tailed test[/C][/ROW]
[ROW][C]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=22480&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22480&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 variance1.2
sample mean15.46
null hypothesis about mean15
type I error0.05
critical value (one-tailed)15.3467655919170
confidence interval (two-tailed)(sample mean)[ 15.0468033117970 , 15.8731966882030 ]
conclusion for one-tailed test
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 = 1.2 ; par3 = 15.46 ; par4 = 15 ; par5 = 0.05 ;
Parameters (R input):
par1 = 27 ; par2 = 1.2 ; par3 = 15.46 ; par4 = 15 ; par5 = 0.05 ;
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')