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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 05:43:11 -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/t12260618231kte7h0gwn9vkcq.htm/, Retrieved Sun, 19 May 2024 04:42:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22482, Retrieved Sun, 19 May 2024 04:42:24 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192

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] [q3] [2008-11-07 12:43:11] [7596afe9a05f2a2719ece78b1b0e12e6] [Current]
Feedback Forum
2008-11-17 10:45:25 [Nicolaj Wuyts] [reply] 
Bij deze vraag gebruik je: testing mean wirh knwon variance - Type II error. De sample size is 27, de population variance is 0,012; de sample mean is 0,1546; de nul hypothese is 0,15; de type I error is 0,05 en de alternatieve hypothese is 0,152. Door deze berekening krijg je een type II error waarde van 0.93942747750307. Dit wil zeggen dat er een kans is van 94% dat we het hoger vet percentage niet zullen opmerken.
2008-11-17 14:09:09 [Stef Vermeiren] [reply] 
Wederom foute input!

http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/13/t1226571334c9eh0kttx1okj7g.htm
Om deze vraag op te lossen moeten we op zoek gaan naar de type 2-error. Met andere woorden, de kans dat het niet ontdekt wordt wanneer er een hoger vetpercentage gebruikt wordt (meer dan 15%).
In dit geval is er ongeveer 94% kans dat de fraude niet ontdekt wordt.
2008-11-24 16:19:08 [4679c4d03f1d346a85e79d87ba60ec2b] [reply] 
Verkeerde methode met verkeerde gegevens. Hier zou de type II error berekent moeten worden om na te gaan of de fraude van de leverancier gedetecteerd kan worden. De population variance zou ook hier 0.012 moeten zijn, de sample mean 0.1546 en de nulhypothese 0.15. De kans dat de leverancier gepakt word is maar 6% en dus zeer weinig.

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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'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=22482&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=22482&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22482&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 variance1.2
sample mean15.46
null hypothesis about mean15.2
type I error0.05
critical value (one-tailed)15.5467655919170
confidence interval (two-tailed)(sample mean)[ 15.0468033117970 , 15.8731966882030 ]
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 & 1.2 \tabularnewline
sample mean & 15.46 \tabularnewline
null hypothesis about mean & 15.2 \tabularnewline
type I error & 0.05 \tabularnewline
critical value (one-tailed) & 15.5467655919170 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 15.0468033117970 ,  15.8731966882030 ] \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=22482&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]15.2[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]15.5467655919170[/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]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=22482&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22482&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 mean15.2
type I error0.05
critical value (one-tailed)15.5467655919170
confidence interval (two-tailed)(sample mean)[ 15.0468033117970 , 15.8731966882030 ]
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 = 1.2 ; par3 = 15.46 ; par4 = 15.2 ; par5 = 0.05 ;
Parameters (R input):
par1 = 27 ; par2 = 1.2 ; par3 = 15.46 ; par4 = 15.2 ; 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')