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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 16:48:04 -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/t1319575722mcwsy66itozhdha.htm/, Retrieved Tue, 10 Feb 2026 04:52:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=136259, Retrieved Tue, 10 Feb 2026 04:52:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact287

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 known Variance - Critical Value] [WS 4 - Task 2] [2011-10-25 20:48:04] [8aedcf735e397266388b06f47fe45218] [Current]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [WS 4 - Task 2 - "T"] [2011-10-25 21:10:02] [7156a20ff7d97880b6dc50f7239ba03b]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [11] [2011-10-25 21:14:17] [7156a20ff7d97880b6dc50f7239ba03b]
-   P       [Testing Mean with unknown Variance - Critical Value] [WS 4 - Task 2 - "T"] [2011-10-25 21:15:38] [7156a20ff7d97880b6dc50f7239ba03b]
-    D        [Testing Mean with unknown Variance - Critical Value] [WS 4 - Task 2 - "E"] [2011-10-25 21:39:54] [7156a20ff7d97880b6dc50f7239ba03b]
-    D        [Testing Mean with unknown Variance - Critical Value] [WS 4 - Task 2 - "S"] [2011-10-25 21:51:06] [7156a20ff7d97880b6dc50f7239ba03b]
-   PD        [Testing Mean with unknown Variance - Critical Value] [WS 4 - Task 4] [2011-10-25 22:30:54] [7156a20ff7d97880b6dc50f7239ba03b]
-   PD        [Testing Mean with unknown Variance - Critical Value] [WS 4 - Task 4] [2011-10-25 22:46:36] [7156a20ff7d97880b6dc50f7239ba03b]
-   PD        [Testing Mean with unknown Variance - Critical Value] [WS 4 - Task 5] [2011-10-25 23:01:51] [7156a20ff7d97880b6dc50f7239ba03b]
- RMPD        [One Sample Tests about the Mean] [WS 4 - Task 7] [2011-10-25 23:26:55] [7156a20ff7d97880b6dc50f7239ba03b]
- RMPD        [One Sample Tests about the Mean] [Workshop1 - Task ...] [2011-10-25 23:41:03] [7156a20ff7d97880b6dc50f7239ba03b]
- RMPD        [Testing Mean with known Variance - Sample Size] [Workshop1 - Task 9] [2011-10-26 00:00:30] [7156a20ff7d97880b6dc50f7239ba03b]
- RMPD        [Testing Mean with known Variance - Sample Size] [Workshop1 - Task 10] [2011-10-26 00:04:28] [7156a20ff7d97880b6dc50f7239ba03b]
- RMPD        [Minimum Sample Size - Testing Mean] [Workshop1 - Task 11] [2011-10-26 00:19:22] [7156a20ff7d97880b6dc50f7239ba03b]
- RMPD        [Testing Variance - Critical Value (Region)] [Workshop 4 - Task...] [2011-10-26 00:27:49] [7156a20ff7d97880b6dc50f7239ba03b]
- RMPD        [Testing Variance - Critical Value (Region)] [Workshop1 - Task ...] [2011-10-26 00:35:24] [7156a20ff7d97880b6dc50f7239ba03b]
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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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=136259&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=136259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136259&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'Herman Ole Andreas Wold' @ wold.wessa.net






Testing Mean with known Variance
sample size9
population variance0.36
sample mean5.35
null hypothesis about mean5.2
type I error0.05
critical value (one-tailed)5.52897072539029
confidence interval (two-tailed)(sample mean)[ 4.95800720309199 , 5.74199279690801 ]
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 & 9 \tabularnewline
population variance & 0.36 \tabularnewline
sample mean & 5.35 \tabularnewline
null hypothesis about mean & 5.2 \tabularnewline
type I error & 0.05 \tabularnewline
critical value (one-tailed) & 5.52897072539029 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 4.95800720309199 ,  5.74199279690801 ] \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=136259&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]9[/C][/ROW]
[ROW][C]population variance[/C][C]0.36[/C][/ROW]
[ROW][C]sample mean[/C][C]5.35[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]5.2[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]5.52897072539029[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 4.95800720309199 ,  5.74199279690801 ][/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=136259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136259&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 size9
population variance0.36
sample mean5.35
null hypothesis about mean5.2
type I error0.05
critical value (one-tailed)5.52897072539029
confidence interval (two-tailed)(sample mean)[ 4.95800720309199 , 5.74199279690801 ]
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 = 9 ; par2 = 0.36 ; par3 = 5.35 ; par4 = 5.2 ; par5 = 0.05 ;
Parameters (R input):
par1 = 9 ; par2 = 0.36 ; par3 = 5.35 ; par4 = 5.2 ; 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')