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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 computationMon, 10 Nov 2008 13:57:50 -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/10/t1226350710kzho0imxclprwkn.htm/, Retrieved Sun, 19 May 2024 09:39:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23200, Retrieved Sun, 19 May 2024 09:39:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163

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] [Case Pork Q1] [2008-11-10 20:57:50] [63db34dadd44fb018112addcdefe949f] [Current]
Feedback Forum
2008-11-18 09:12:27 [Ellen Smolders] [reply] 
De student heeft de juiste berekeningen gemaakt maar zijn antwoord is niet volledig correct. Om te beginnen is het niet verplicht eenzijdige test te nemen, de argumentatie van de student voor de eenzijdige test is correct. Toch kunnen we ook een tweezijdige test gebruiken omdat een te laag vetpercentage ook ongezond is voor de mens, maar dit is minder vanzelfsprekend. Voor de rest kunnen we zien dat de sample mean (0.1546) langs twee kanten binnen het betrouwbaarheidsinterval valt, nl. 0.113280.. en 0.195919… We kunnen zien dat de sample mean wel iets boven de critical value ligt, maar deze afwijking is te klein om een niet toevallig te zijn. (dit heeft de student ook verkeerd geïnterpreteerd, de sample mean overschrijft de critical value WEL). We verwerpen de nullhypothese niet omdat de waarden conform het contract zijn.
2008-11-20 15:12:25 [Els Keysers] [reply] 
Sample mean 0.1546 < critical value 0.184676559191704
De sample mean ligt NIET boven de critical value.
2008-11-21 11:08:09 [Evelien Blockx] [reply] 
De berekening is helemaal juist uitgevoerd.
Toch zou ik geen klacht indienen, ook al is een vetgehalte bepaald in het contract. Het kan immers gebeuren dat er een kleine toevallige afwijking is.

Hier ligt het steekproefgemiddelde onder de critical value, dus het gaat hier om een toevallige afwijking.

Je kiest hier voor one tailed. Dat is correct, want je hebt er een goede verantwoording voor.

Je zou ook kunnen kiezen voor two tailed, maar dan zou je een andere verantwoording moeten gebruiken. Dan wordt zowel de afwijking naar boven als de afwijking naar beneden gemeten, omdat het niet goed is dat er teveel vetgehalte is, maar het is ook niet goed dat er te weinig vetgehalte is, want dat zou de kwaliteit van het vlees ook niet ten goede komen.

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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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23200&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23200&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Testing Mean with known Variance
sample size27
population variance0.012
sample mean0.1546
null hypothesis about mean0.15
type I error0.05
critical value (one-tailed)0.184676559191704
confidence interval (two-tailed)(sample mean)[ 0.113280331179696 , 0.195919668820304 ]
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 & 0.012 \tabularnewline
sample mean & 0.1546 \tabularnewline
null hypothesis about mean & 0.15 \tabularnewline
type I error & 0.05 \tabularnewline
critical value (one-tailed) & 0.184676559191704 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 0.113280331179696 ,  0.195919668820304 ] \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=23200&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]0.05[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]0.184676559191704[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 0.113280331179696 ,  0.195919668820304 ][/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=23200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23200&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 error0.05
critical value (one-tailed)0.184676559191704
confidence interval (two-tailed)(sample mean)[ 0.113280331179696 , 0.195919668820304 ]
conclusion for one-tailed test
Do not reject the null hypothesis.
conclusion for two-tailed test
Do not 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 = 0.05 ;
Parameters (R input):
par1 = 27 ; par2 = 0.012 ; par3 = 0.1546 ; par4 = 0.15 ; 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')