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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_hypothesismean2.wasp

Title produced by software

Testing Mean with known Variance - p-value

Date of computation

Mon, 28 Oct 2013 12:18:59 -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/28/t1382977149ydiq6ppufkcvo7m.htm/, Retrieved Thu, 12 Feb 2026 14:44:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=220166, Retrieved Thu, 12 Feb 2026 14:44:26 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

296

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]
-   PD    [Testing Mean with unknown Variance - Critical Value] [WS4 - Question 5] [2010-10-25 19:47:30] [1f5baf2b24e732d76900bb8178fc04e7]
- RMPD      [Testing Mean with known Variance - Critical Value] [WS4 - Question 8 ...] [2010-10-25 20:19:30] [1f5baf2b24e732d76900bb8178fc04e7]
F R P         [Testing Mean with known Variance - Critical Value] [ws4 Q8 (females)] [2010-10-26 18:22:26] [afe9379cca749d06b3d6872e02cc47ed]
- RMP           [Testing Mean with known Variance - p-value] [Question 8] [2013-10-28 16:10:06] [fcc5c79267206050edde2804b94bb45f]
- R                 [Testing Mean with known Variance - p-value] [] [2013-10-28 16:18:59] [2248f9356ab384c90566acb3246d93bf] [Current]
- RM                  [Testing Mean with known Variance - Sample Size] [] [2013-10-28 16:21:00] [fcc5c79267206050edde2804b94bb45f] 
- RM                  [Testing Mean with known Variance - Sample Size] [] [2013-10-28 16:22:56] [fcc5c79267206050edde2804b94bb45f] 
- RMP                   [Testing Mean with known Variance - Sample Size] [] [2013-10-30 18:54:02] [28b01683adeed0ece37c11d0e0637e9d] 

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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	0 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 0 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=220166&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=220166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220166&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	0 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Testing Mean with known Variance
sample size	63
population variance	0.13
sample mean	21.1587301587302
null hypothesis about mean	20
type I error	0.35
Z-value	25.5082643602343
p-value (one-tailed)	0
p-value (two-tailed)	0
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 & 63 \tabularnewline
population variance & 0.13 \tabularnewline
sample mean & 21.1587301587302 \tabularnewline
null hypothesis about mean & 20 \tabularnewline
type I error & 0.35 \tabularnewline
Z-value & 25.5082643602343 \tabularnewline
p-value (one-tailed) & 0 \tabularnewline
p-value (two-tailed) & 0 \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=220166&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]63[/C][/ROW]
[ROW][C]population variance[/C][C]0.13[/C][/ROW]
[ROW][C]sample mean[/C][C]21.1587301587302[/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]Z-value[/C][C]25.5082643602343[/C][/ROW]
[ROW][C]p-value (one-tailed)[/C][C]0[/C][/ROW]
[ROW][C]p-value (two-tailed)[/C][C]0[/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=220166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=220166&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	63
population variance	0.13
sample mean	21.1587301587302
null hypothesis about mean	20
type I error	0.35
Z-value	25.5082643602343
p-value (one-tailed)	0
p-value (two-tailed)	0
conclusion for one-tailed test
Reject the null hypothesis.
conclusion for two-tailed test
Reject the null hypothesis

Parameters (Session):

par1 = 0.98 ; par2 = 20 ;

Parameters (R input):

par1 = 63 ; par2 = 0.13 ; par3 = 21.1587301587302 ; 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))
z <- (par3 - par4) / (sqrt(par2/par1))
p <- 1-pnorm(z)
if (par3 == par4)
{
conclusion <- 'Error: the null hypothesis and sample mean must not be equal.'
conclusion2 <- conclusion
} else {
if (p < par5/2)
{
conclusion2 <- 'Reject the null hypothesis'
} else {
conclusion2 <- 'Do not reject the null hypothesis'
}
}
if (p < par5)
{
conclusion <- 'Reject the null hypothesis.'
} else {
conclusion <- 'Do not reject the null hypothesis.'
}
p
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,'Z-value',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (one-tailed)',header=TRUE)
a<-table.element(a,p)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (two-tailed)',header=TRUE)
a<-table.element(a,p*2)
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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code