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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 computationSat, 26 Oct 2013 08:26:58 -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/2013/Oct/26/t1382790436j4qavm78re4b9zg.htm/, Retrieved Tue, 10 Feb 2026 09:26:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=219622, Retrieved Tue, 10 Feb 2026 09:26:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact294

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Testing Mean with unknown Variance - Critical Value] [WS 4 Q 4] [2011-10-22 13:22:14] [a9671b130b33f9fcb98554992ce4582f]
- RMPD  [One Sample Tests about the Mean] [WS 4 Q 7] [2011-10-22 13:30:48] [a9671b130b33f9fcb98554992ce4582f]
- RMPD      [Testing Mean with known Variance - Critical Value] [] [2013-10-26 12:26:58] [a5501fab9c787febb2a952032c60b28f] [Current]
- R P         [Testing Mean with known Variance - Critical Value] [] [2013-10-26 12:31:28] [4d39cf209776852399955073f9d0ee7a]
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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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219622&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219622&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219622&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'Sir Maurice George Kendall' @ kendall.wessa.net






Testing Mean with known Variance
sample size98
population variance3.60555127546399
sample mean20.2857142857143
null hypothesis about mean20
type I error0.35
critical value (one-tailed)20.0739085832745
confidence interval (two-tailed)(sample mean)[ 20.1064500719788 , 20.4649784994498 ]
conclusion for one-tailed test
Reject the null hypothesis.
conclusion for two-tailed test
Reject the null hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
sample size & 98 \tabularnewline
population variance & 3.60555127546399 \tabularnewline
sample mean & 20.2857142857143 \tabularnewline
null hypothesis about mean & 20 \tabularnewline
type I error & 0.35 \tabularnewline
critical value (one-tailed) & 20.0739085832745 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 20.1064500719788 ,  20.4649784994498 ] \tabularnewline
conclusion for one-tailed test \tabularnewline
Reject the null hypothesis. \tabularnewline
conclusion for two-tailed test \tabularnewline
Reject the null hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219622&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]3.60555127546399[/C][/ROW]
[ROW][C]sample mean[/C][C]20.2857142857143[/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]20.0739085832745[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 20.1064500719788 ,  20.4649784994498 ][/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]Reject the null hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219622&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219622&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 variance3.60555127546399
sample mean20.2857142857143
null hypothesis about mean20
type I error0.35
critical value (one-tailed)20.0739085832745
confidence interval (two-tailed)(sample mean)[ 20.1064500719788 , 20.4649784994498 ]
conclusion for one-tailed test
Reject the null hypothesis.
conclusion for two-tailed test
Reject the null hypothesis


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 98 ; par2 = 3.605551275463989 ; par3 = 20.2857142857143 ; par4 = 20 ; par5 = 0.35 ;
Parameters (R input):
par1 = 98 ; par2 = 3.605551275463989 ; par3 = 20.2857142857143 ; par4 = 20 ; par5 = 0.35 ;
R code (references can be found in the software module):
par5 <- '0.35'
par4 <- '20'
par3 <- '20.2857142857143'
par2 <- '3,605551275463989'
par1 <- '98'
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')