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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 computationTue, 04 Nov 2008 04:51:07 -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/04/t1225799536kmbqpvkldyladot.htm/, Retrieved Sun, 19 May 2024 07:11:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21497, Retrieved Sun, 19 May 2024 07:11:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155

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] [2008-11-04 11:51:07] [5f3e73ccf1ddc75508eed47fa51813d3] [Current]
Feedback Forum
2008-11-20 13:53:21 [Kim Huysmans] [reply] 
Het antwoord is correct. Met een type I error van 5% is het gemiddelde kleiner dan de critical value, wat wil zeggen dat het gemiddelde van de stalen (15,46%) de critical value (18,47  de nieuwe grens die we bekomen door een type I error van 5% te aanvaarden) niet overschrijdt dus moeten we geen klacht indienen.
De twee zijdige methode had hier ook van toepassing kunnen zijn. De sample mean ligt namelijk binnen het betrouwbaarheidsinterval.
2008-11-21 15:34:09 [Dries Van Gheluwe] [reply] 
Het antwoord is inderdaad correct maar je kiest voor een 1 sided test omdat je enkel nut hebt om te weten of het vetgehalte boven 15 % ligt en niet eronder. Je moet niet weten hoeveel percent het eronder ligt.
2008-11-23 13:44:44 [339a57d8a4d5d113e4804fc423e4a59e] [reply] 
De student heeft de juiste berekeningssoftware gebruikt. De analyse mocht echter uitgebreider. De critical value is groter dan het gemiddelde, waardoor er geen signifacant verschil is. Er is dus sprake van toeval. We moeten dus geen klacht indienen. De 0 hypothese wordt aanvaard.

Men kan hier zowel 1sided als 2sided gebruiken.
2008-11-24 17:18:39 [Thomas Beyers] [reply] 
2008-11-24 17:19:06 [Thomas Beyers] [reply] 
Kies voor one-sided: omdat de leverancier enkel daar een economisch voordeel kan halen. De one-sided test meet de afwijking naar boven.

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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=21497&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=21497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21497&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 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=21497&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=21497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21497&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')