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Author

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R Software Module

rwasp_hypothesismean3.wasp

Title produced by software

Testing Mean with known Variance - Type II Error

Date of computation

Thu, 06 Nov 2008 05:38:52 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/06/t12259752087mck78wq4j9k5fx.htm/, Retrieved Fri, 13 Feb 2026 11:50:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22071, Retrieved Fri, 13 Feb 2026 11:50:50 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

369

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F       [Testing Mean with known Variance - Type II Error] [Case: the Pork Qu...] [2008-11-06 12:38:52] [284c7cdb9fcda2adcbb08e211682c8d6] [Current]
F RMP     [Testing Mean with known Variance - Sample Size] [Case: the Pork Qu...] [2008-11-06 13:00:43] [38f43994ada0e6172896e12525dcc585] 
F           [Testing Mean with known Variance - Sample Size] [PorkQT Q4] [2008-11-11 21:04:30] [d32f94eec6fe2d8c421bd223368a5ced] 
- RMP     [Testing Sample Mean with known Variance - Confidence Interval] [ the Pork Quality...] [2008-11-06 13:19:48] [5393e1e70f7d2761ff95f84c9c07decf] 
F RMP     [Testing Sample Mean with known Variance - Confidence Interval] [Case: the Pork Qu...] [2008-11-06 13:30:45] [82970caad4b026be9dd352fdec547fe4] 
F           [Testing Sample Mean with known Variance - Confidence Interval] [PorkQT Q6] [2008-11-11 21:09:08] [d32f94eec6fe2d8c421bd223368a5ced] 
F RMP     [Testing Population Mean with known Variance - Confidence Interval] [Case: the Pork Qu...] [2008-11-06 13:36:00] [82970caad4b026be9dd352fdec547fe4] 
F           [Testing Population Mean with known Variance - Confidence Interval] [PorkQT Q5] [2008-11-11 21:06:58] [d32f94eec6fe2d8c421bd223368a5ced] 
F         [Testing Mean with known Variance - Type II Error] [PorkQT Q3] [2008-11-11 21:01:51] [d32f94eec6fe2d8c421bd223368a5ced] 

Feedback Forum

2008-11-15 17:53:03 [Kevin Neelen] [reply] 
Er is hier gebruik gemaakt van de juiste methode om deze vraagstelling te kunnen oplossen, namelijk 'Testing Mean with known Variance - Type II Error'. 
Uit deze tabel kunnen we afleiden dat bij het type II error, de kans dat de fraude niet opgemerkt wordt, bijna 94% bedraagt. De pakkans is dus net iets groter dan 6%.  
De conclusie van deze student dat er een kleine pakkans bestaat, is bijgevolg correct.
2008-11-21 22:35:38 [Kim Wester] [reply] 
De kans dat de leverancier bij veroordeling vrij wordt gesproken (ondanks fraude) is 94% (0.93942747750307). De kans dat de leverancier bij veroordeling wordt gepakt op fraude is dus 6%. 
 
Deze conclusie is alleen geldig wanneer wij de oud-werknemer volledig vertrouwen!
2008-11-24 22:48:32 [Martjin De Swert] [reply] 
De student gebruikt de correcte manier om de vraag te beantwoorden. Dankzij de techniek van Testing Mean With Known Variance - Type II Error komen we te weten dat de kans dat de fraude onopgemerkt gebeurt ongeveer 94% (0.93942747750307) bedraagt. De producent loopt maw maar een kans van ongeveer 6% op betrapping.

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22071&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22071&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22071&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Testing Mean with known Variance
sample size	27
population variance	0.012
sample mean	0.1546
null hypothesis about mean	0.15
type I error	0.05
alternative hypothesis about mean	0.152
Type II Error	0.93942747750307

\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
alternative hypothesis about mean & 0.152 \tabularnewline
Type II Error & 0.93942747750307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22071&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]alternative hypothesis about mean[/C][C]0.152[/C][/ROW]
[ROW][C]Type II Error[/C][C]0.93942747750307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22071&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22071&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 size	27
population variance	0.012
sample mean	0.1546
null hypothesis about mean	0.15
type I error	0.05
alternative hypothesis about mean	0.152
Type II Error	0.93942747750307

Parameters (Session):

par1 = 27 ; par2 = 0.012 ; par3 = 0.1546 ; par4 = 0.15 ; par5 = 0.05 ; par6 = 0.152 ;

Parameters (R input):

par1 = 27 ; par2 = 0.012 ; par3 = 0.1546 ; par4 = 0.15 ; par5 = 0.05 ; par6 = 0.152 ;

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)
par6<-as.numeric(par6)
c <- 'NA'
csn <- abs(qnorm(par5))
if (par3 == par4)
{
conclusion <- 'Error: the null hypothesis and sample mean must not be equal.'
}
if (par3 > par4)
{
c <- par4 + csn * sqrt(par2) / sqrt(par1)
}
if (par3 < par4)
{
c <- par4 - csn * sqrt(par2) / sqrt(par1)
}
p <- pnorm((c - par6) / (sqrt(par2/par1)))
p
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,'alternative hypothesis about mean',header=TRUE)
a<-table.element(a,par6)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm#ex3','Type II Error','example'),header=TRUE)
a<-table.element(a,p)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')

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Input Parameters & R Code