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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 computationThu, 13 Nov 2008 07:49:41 -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/13/t1226587813zlfjuoxp8ydl9st.htm/, Retrieved Mon, 20 May 2024 10:09:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24633, Retrieved Mon, 20 May 2024 10:09:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Box-Cox Linearity Plot] [question 3 box-co...] [2008-11-12 15:13:33] [31c9f333c18b3396ccf9d2485dd39c8a]
F RMPD  [Maximum-likelihood Fitting - Normal Distribution] [question 5] [2008-11-12 15:49:20] [31c9f333c18b3396ccf9d2485dd39c8a]
F RMPD      [Testing Mean with known Variance - Critical Value] [question 3] [2008-11-13 14:49:41] [490fee4f334e2e025c95681783e3fd0b] [Current]
Feedback Forum
2008-11-22 15:17:34 [6066575aa30c0611e452e930b1dff53d] [reply] 
De output produced by software is verkeerd. De populatie variantie moet gelijk zijn aan 0.012. De sample mean moet gelijk zijn aan 0.1546. De nulhypothese moet gelijk zijn aan 0.15. Verder heeft hij ook hier de verkeerde tabel gebruikt om deze vraag te bespreken. Je moet hier testing mean with known variance gebruiken waaruit de type II error berekend wordt. De conclusie is hier bijgevolg ook fout. De correcte conclusie is dat de waarschijnlijkheid dat we er niet achter zullen komen dat de productie van varkensvlees 15.2% is in plaats van 15% is 93,94%. Er is dus een zeer grote kans dat we er niet achter komen. De pakkans is dus slechts 6%.
2008-11-22 19:01:19 [c00776cbed2786c9c4960950021bd861] [reply] 
De tabel die de studen(e) gebruikt heeft bij Q2 hoort eigenlijk bij deze vraag. Want de uitkomst van typeII error is belangrijk om hier een conslusie te formuleren.
In de vraag staat : ‘wat is de kans dat we de fraude niet detecteren’, wat wijst op een type II error. Deze kunnen aflezen uit de tabel, nl. 0.939427…
Er is dus een zeer grote kans dat we de fraude niet vinden/detecteren.
  2008-11-22 19:02:49 [c00776cbed2786c9c4960950021bd861] [reply] 
In de tabel werden wel verkeerde cijfers gebruikt --> zie feedback Q1
2008-11-24 15:45:21 [4679c4d03f1d346a85e79d87ba60ec2b] [reply] 
Verkeerde methode en verkeerde gegevens. De type II error is niet berekend. Deze is nodig bij deze vraag om na te gaan hoe groot de kans is dat de fraude van de leverancier niet ontdekt kan worden. De type II error is hier 94%, maw de kans dat de leverancier vrij kan frauderen is 94% en dus enorm hoog.

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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=24633&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=24633&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24633&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 mean15.47
null hypothesis about mean15.2
type I error0.05
critical value (one-tailed)15.5467655919170
confidence interval (two-tailed)(sample mean)[ 15.0568033117970 , 15.8831966882030 ]
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 & 15.47 \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) & [ 15.0568033117970 ,  15.8831966882030 ] \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=24633&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]15.47[/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][ 15.0568033117970 ,  15.8831966882030 ][/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=24633&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24633&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 mean15.47
null hypothesis about mean15.2
type I error0.05
critical value (one-tailed)15.5467655919170
confidence interval (two-tailed)(sample mean)[ 15.0568033117970 , 15.8831966882030 ]
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 = 15.47 ; par4 = 15.2 ; par5 = 0.05 ;
Parameters (R input):
par1 = 27 ; par2 = 1.2 ; par3 = 15.47 ; 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')