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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 computationTue, 11 Nov 2008 10:58:28 -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/11/t1226426352lcuslvbj9yd1wzi.htm/, Retrieved Sun, 19 May 2024 10:51:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23785, Retrieved Sun, 19 May 2024 10:51:16 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
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] [] [2008-11-11 12:18:34] [2a0ad3a9bcadca2da0acb91636601c6c]
F         [Testing Mean with known Variance - Critical Value] [] [2008-11-11 17:58:28] [428345b1a3979ee2ad6751f9aac15fbb] [Current]
Feedback Forum
2008-11-20 22:34:26 [256f97d8b7c07ed49f142eff724c6520] [reply
Goed, extra aanvulling: we gebruiken de eenzijdige test omdat we verwachten dat d e leverancier meer dan het gemiddelde vet in het vlees zou doen.
De nul hypothese verwerpen we niet omdat de sample mean inderdaad de critical value niet overschrijdt.
2008-11-21 12:07:38 [Peter Melgers] [reply
Deze oplossing is fout!

De population variance is 0.012 ipv 0.12.

De kritieke waarde ligt lager nl. 0.1846....

Het besluit dat je getrokken hebt kan dus nooit uit deze tabel geweest zijn...

We kunnen concluderen dat zelfs indien we uitgaan van een nullhypothese van 15.2%, het steekproefgemiddelde (15.46%) nog altijd lager ligt dan de bekomen waarde 18.66% en dus nog altijd binnen het 95%-betrouwbaarheidsinterval valt.

Enkel de afwijking naar boven levert economisch voordeel op voor de producent daarom pakken we het one-sided confidence interval. Het gebruik van een two-sided confidence interval zou echter ook juist zijn.
2008-11-21 12:11:14 [Peter Melgers] [reply
De volgende oplossing is juist (het laatste stuk van mijn vorige post was verkeerd gekopieerd):

We zouden ook de two-tailed test kunnen gebruiken omdat de afwijking zowel naar boven als naar beneden mogelijk kan zijn (er kan zowel te veel vet in het vlees zitten als te weinig vet). Hierbij kunnen we ook zien dat het steekproefgemiddelde van 15.46% in het betrouwbaarheidsinterval valt.

De one-sided test zou in dit geval wel voldoende zijn geweest omdat de leverancier enkel economisch voordeel haalt indien hij meer vet in zijn vlees heeft zitten (vet is goedkoper dan vlees).

We gaan de null-hypothese niet verwerpen, alles gebeurd conform het contract.

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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=23785&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=23785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23785&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 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 variance0.12
sample mean0.1546
null hypothesis about mean0.15
type I error0.05
critical value (one-tailed)0.259656908463431
confidence interval (two-tailed)(sample mean)[ 0.0239357343639964 , 0.285264265636004 ]
conclusion for one-tailed test
Do not reject the null hypothesis.
conclusion for two-tailed test
Do not reject the null hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
sample size & 27 \tabularnewline
population variance & 0.12 \tabularnewline
sample mean & 0.1546 \tabularnewline
null hypothesis about mean & 0.15 \tabularnewline
type I error & 0.05 \tabularnewline
critical value (one-tailed) & 0.259656908463431 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 0.0239357343639964 ,  0.285264265636004 ] \tabularnewline
conclusion for one-tailed test \tabularnewline
Do not reject the null hypothesis. \tabularnewline
conclusion for two-tailed test \tabularnewline
Do not reject the null hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23785&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]0.12[/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]0.05[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]0.259656908463431[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 0.0239357343639964 ,  0.285264265636004 ][/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]Do not reject the null hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23785&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Testing Mean with known Variance
sample size27
population variance0.12
sample mean0.1546
null hypothesis about mean0.15
type I error0.05
critical value (one-tailed)0.259656908463431
confidence interval (two-tailed)(sample mean)[ 0.0239357343639964 , 0.285264265636004 ]
conclusion for one-tailed test
Do not reject the null hypothesis.
conclusion for two-tailed test
Do not reject the null hypothesis



Parameters (Session):
par1 = 27 ; par2 = 0.12 ; par3 = 0.1546 ; par4 = 0.15 ; par5 = 0.05 ;
Parameters (R input):
par1 = 27 ; par2 = 0.12 ; par3 = 0.1546 ; par4 = 0.15 ; par5 = 0.05 ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')