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R Software Module

rwasp_hypothesismean1.wasp

Title produced by software

Testing Mean with known Variance - Critical Value

Date of computation

Tue, 29 Oct 2013 06:10:19 -0400

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/2013/Oct/29/t1383041439nggku2ewtmaj79f.htm/, Retrieved Thu, 12 Feb 2026 09:30:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=220448, Retrieved Thu, 12 Feb 2026 09:30:18 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

360

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] [Workshop 4 - vraa...] [2013-10-29 10:10:19] [47fc20d512b54de2decb1f477fea32db] [Current]
- R P     [Testing Mean with known Variance - Critical Value] [Workshop 4 - vraa...] [2013-10-29 10:13:42] [6e6101806504d86600f236fbba4f8aec] 
- RMP     [Testing Mean with known Variance - Sample Size] [Workshop 4 - vraag 9] [2013-10-29 10:19:43] [6e6101806504d86600f236fbba4f8aec] 
- R P       [Testing Mean with known Variance - Sample Size] [Workshop 4 - vraa...] [2013-10-29 10:21:41] [6e6101806504d86600f236fbba4f8aec] 
-   P         [Testing Mean with known Variance - Sample Size] [Workshop 4 - vraa...] [2013-10-29 10:25:36] [6e6101806504d86600f236fbba4f8aec] 
-   P           [Testing Mean with known Variance - Sample Size] [Workshop 4 - vraa...] [2013-10-30 18:27:16] [6e6101806504d86600f236fbba4f8aec] 
- RMP           [Minimum Sample Size - Testing Mean] [Workshop 4 - vraa...] [2013-10-30 18:28:44] [6e6101806504d86600f236fbba4f8aec] 
- RMP         [Minimum Sample Size - Testing Mean] [Workshop 4 - vraa...] [2013-10-29 10:29:10] [6e6101806504d86600f236fbba4f8aec] 
-   P         [Testing Mean with known Variance - Sample Size] [Workshop 4 - vraa...] [2013-10-30 18:26:06] [6e6101806504d86600f236fbba4f8aec] 

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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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=220448&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=220448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220448&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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Testing Mean with known Variance
sample size	98
population variance	0.87
sample mean	20.29
null hypothesis about mean	0
type I error	0.65
critical value (one-tailed)	0.0363051859727149
confidence interval (two-tailed)(sample mean)	[ 20.2472461830146 , 20.3327538169854 ]
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 & 0.87 \tabularnewline
sample mean & 20.29 \tabularnewline
null hypothesis about mean & 0 \tabularnewline
type I error & 0.65 \tabularnewline
critical value (one-tailed) & 0.0363051859727149 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 20.2472461830146 ,  20.3327538169854 ] \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=220448&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]0.87[/C][/ROW]
[ROW][C]sample mean[/C][C]20.29[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]0[/C][/ROW]
[ROW][C]type I error[/C][C]0.65[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]0.0363051859727149[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 20.2472461830146 ,  20.3327538169854 ][/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=220448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220448&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	98
population variance	0.87
sample mean	20.29
null hypothesis about mean	0
type I error	0.65
critical value (one-tailed)	0.0363051859727149
confidence interval (two-tailed)(sample mean)	[ 20.2472461830146 , 20.3327538169854 ]
conclusion for one-tailed test
Reject the null hypothesis.
conclusion for two-tailed test
Reject the null hypothesis

Parameters (Session):

par1 = 98 ; par2 = 0.87 ; par3 = 20.29 ; par4 = 0 ; par5 = 0.65 ;

Parameters (R input):

par1 = 98 ; par2 = 0.87 ; par3 = 20.29 ; par4 = 0 ; par5 = 0.65 ;

R code (references can be found in the software module):

par5 <- '0.65'
par4 <- '0'
par3 <- '20.29'
par2 <- '0.87'
par1 <- '9'
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')

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