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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 04:50:48 -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/t1225799516ro6jpfp5cxdg1l7.htm/, Retrieved Sun, 15 Feb 2026 01:49:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21496, Retrieved Sun, 15 Feb 2026 01:49:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact450

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 11:50:48] [b4fc5040f26b33db57f84cfb8d1d2b82] [Current]
F         [Testing Mean with known Variance - Critical Value] [Case the Pork Qua...] [2008-11-09 10:12:07] [063e4b67ad7d3a8a83eccec794cd5aa7]
F RM      [Testing Mean with known Variance - p-value] [Case the Pork Qua...] [2008-11-09 10:16:47] [063e4b67ad7d3a8a83eccec794cd5aa7]
F RMP     [Testing Mean with known Variance - Type II Error] [Case the Pork Qua...] [2008-11-09 10:21:59] [063e4b67ad7d3a8a83eccec794cd5aa7]
F RMP     [Testing Mean with known Variance - Sample Size] [Case the Pork Qua...] [2008-11-09 10:24:37] [063e4b67ad7d3a8a83eccec794cd5aa7]
F RMP     [Testing Sample Mean with known Variance - Confidence Interval] [Case the Pork Qua...] [2008-11-09 10:28:17] [063e4b67ad7d3a8a83eccec794cd5aa7]
F RMP     [Testing Sample Mean with known Variance - Confidence Interval] [Case the Pork Qua...] [2008-11-09 10:30:38] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Variance - Critical Value (Region)] [Various types of ...] [2008-11-09 10:44:06] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Variance - Critical Value (Region)] [Various types of ...] [2008-11-09 10:45:33] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Variance - p-value (probability)] [Various types of ...] [2008-11-09 10:46:43] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Variance - p-value (probability)] [Various types of ...] [2008-11-09 10:47:46] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Variance - Confidence Intervals for Sample Variance] [Various types of ...] [2008-11-09 10:49:04] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Variance - Confidence Intervals for Sample Variance] [Various types of ...] [2008-11-09 10:50:24] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Variance - Confidence Intervals for Population Variance] [Various types of ...] [2008-11-09 10:51:36] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Variance - Confidence Intervals for Population Variance] [Various types of ...] [2008-11-09 10:52:26] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Testing Population Proportion - Critical Value] [Various types of ...] [2008-11-09 11:02:05] [063e4b67ad7d3a8a83eccec794cd5aa7]
- RMP     [Minimum Sample Size - Testing Proportions] [Various types of ...] [2008-11-09 11:05:09] [063e4b67ad7d3a8a83eccec794cd5aa7]
F         [Testing Mean with known Variance - Critical Value] [] [2008-11-11 20:06:59] [d2d412c7f4d35ffbf5ee5ee89db327d4]
Feedback Forum
2008-11-19 15:31:16 [Gregory Van Overmeiren] [reply] 
We kunnen idd afleiden dat er sprake is van een toevallige afwijking ten opzichte van het contractueel bepaalde vetgehalte (15%). De nullhypothese wordt aanvaard, dit is conform het contract, dus er is niets aan de hand. => geen klacht indienen.
2008-11-23 10:29:46 [Liese Tormans] [reply] 
Het antwoord van de studente is correct maar het is ook mogelijk om dit optelossen m.b.v. het 2-zijdige betrouwbaarheidsinterval, ze heeft gebruik gemaakt van een van de twee mogelijkheden nl het 1-zijdig interval. De hogere waarde is enkel te wijten aan toeval, we mogen de nul hypothese dus niet verwerpen.

Je had deze vraag ook nog kunnen uitvoeren aan de hand van het twee zijdige betrouwbaarheidsinterval.

Want te veel vet is niet goed maar te weinig vet ook niet. We zien dat de sample mean tussen het betrouwbaarheidsinterval [ 0.113280331179696 , 0.195919668820304 ] ligt. Er is dus geen significant verschil. We mogen ook hier de nulhypothese niet verwerpen

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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 time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21496&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]0 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=21496&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21496&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 time0 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=21496&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=21496&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21496&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')