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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, 25 Oct 2011 04:57:35 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/25/t131953322864t61ga6s5e588d.htm/, Retrieved Sat, 25 Apr 2026 21:47:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=135223, Retrieved Sat, 25 Apr 2026 21:47:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact303

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Factor Analysis] [Sleep in Mammals ...] [2010-03-21 11:39:53] [b98453cac15ba1066b407e146608df68]
- RMPD  [Testing Mean with unknown Variance - Critical Value] [Hypothesis Test a...] [2010-10-19 11:45:26] [b98453cac15ba1066b407e146608df68]
- R PD    [Testing Mean with unknown Variance - Critical Value] [WS4 Task 4] [2011-10-25 08:17:16] [8501ca4b76170905b8a207a77f626994]
- RMPD      [Testing Mean with known Variance - Critical Value] [WS4 Task 6] [2011-10-25 08:39:13] [8501ca4b76170905b8a207a77f626994]
- R P           [Testing Mean with known Variance - Critical Value] [WS4 TAsk 8] [2011-10-25 08:57:35] [5ecdd7f9023ba8f0fbc3191d3a9c3da8] [Current]
-   P             [Testing Mean with known Variance - Critical Value] [W task 8S] [2011-10-25 09:01:50] [8501ca4b76170905b8a207a77f626994]
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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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=135223&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=135223&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=135223&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' @ jenkins.wessa.net






Testing Mean with known Variance
sample size98
population variance13
sample mean20.28571429
null hypothesis about mean20
type I error0.35
critical value (one-tailed)20.1403397555142
confidence interval (two-tailed)(sample mean)[ 19.9453222162587 , 20.6261063637413 ]
conclusion for one-tailed test
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 & 98 \tabularnewline
population variance & 13 \tabularnewline
sample mean & 20.28571429 \tabularnewline
null hypothesis about mean & 20 \tabularnewline
type I error & 0.35 \tabularnewline
critical value (one-tailed) & 20.1403397555142 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 19.9453222162587 ,  20.6261063637413 ] \tabularnewline
conclusion for one-tailed test \tabularnewline
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=135223&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]98[/C][/ROW]
[ROW][C]population variance[/C][C]13[/C][/ROW]
[ROW][C]sample mean[/C][C]20.28571429[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]20[/C][/ROW]
[ROW][C]type I error[/C][C]0.35[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]20.1403397555142[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 19.9453222162587 ,  20.6261063637413 ][/C][/ROW]
[ROW][C]conclusion for one-tailed test[/C][/ROW]
[ROW][C]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=135223&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=135223&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 size98
population variance13
sample mean20.28571429
null hypothesis about mean20
type I error0.35
critical value (one-tailed)20.1403397555142
confidence interval (two-tailed)(sample mean)[ 19.9453222162587 , 20.6261063637413 ]
conclusion for one-tailed test
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 = 98 ; par2 = 13 ; par3 = 20.28571429 ; par4 = 20 ; par5 = 0.35 ;
Parameters (R input):
par1 = 98 ; par2 = 13 ; par3 = 20.28571429 ; par4 = 20 ; par5 = 0.35 ;
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')