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Author

*The author of this computation has been verified*

R Software Module

rwasp_hypothesismean4.wasp

Title produced by software

Testing Mean with known Variance - Sample Size

Date of computation

Fri, 19 Oct 2012 09:12:30 -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/2012/Oct/19/t1350652375nns2k3muga3wp8s.htm/, Retrieved Tue, 10 Feb 2026 11:37:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180141, Retrieved Tue, 10 Feb 2026 11:37:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

271

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] [Q1 - A] [2012-10-19 10:57:04] [f4f48270c576c45d216b84daa061a85b]
- RMP   [One Sample Tests about the Mean] [Q2-A] [2012-10-19 11:09:59] [f4f48270c576c45d216b84daa061a85b]
-   PD    [One Sample Tests about the Mean] [Q3-A] [2012-10-19 11:55:37] [f4f48270c576c45d216b84daa061a85b]
- R  D      [One Sample Tests about the Mean] [Q3-B] [2012-10-19 11:59:28] [f4f48270c576c45d216b84daa061a85b]
- R PD        [One Sample Tests about the Mean] [Q6-B] [2012-10-19 12:22:08] [f4f48270c576c45d216b84daa061a85b]
- RMPD            [Testing Mean with known Variance - Sample Size] [Q9-A] [2012-10-19 13:12:30] [78cbff3691fb0cc454e192ff02249329] [Current]
- R                 [Testing Mean with known Variance - Sample Size] [Q10] [2012-10-19 13:15:37] [f4f48270c576c45d216b84daa061a85b] 

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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	'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180141&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180141&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	'Gertrude Mary Cox' @ cox.wessa.net

Testing Mean with known Variance
population variance	13
null hypothesis about mean	20
alternative hypothesis about mean	21
type I error	0.05
type II error	0.05
sample size	140.688259612962

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
population variance & 13 \tabularnewline
null hypothesis about mean & 20 \tabularnewline
alternative hypothesis about mean & 21 \tabularnewline
type I error & 0.05 \tabularnewline
type II error & 0.05 \tabularnewline
sample size & 140.688259612962 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180141&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]population variance[/C][C]13[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]20[/C][/ROW]
[ROW][C]alternative hypothesis about mean[/C][C]21[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]type II error[/C][C]0.05[/C][/ROW]
[ROW][C]sample size[/C][C]140.688259612962[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180141&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
population variance	13
null hypothesis about mean	20
alternative hypothesis about mean	21
type I error	0.05
type II error	0.05
sample size	140.688259612962

Parameters (Session):

Parameters (R input):

par1 = 13 ; par2 = 20 ; par3 = 21 ; par4 = 0.05 ; 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))
if (par2 == par3)
{
conclusion <- 'Error: the null hypothesis and alternative hypothesis must not be equal.'
}
ua <- abs(qnorm(par4))
ub <- qnorm(par5)
c <- (par2+ua/ub*(-par3))/(1-(ua/ub))
sqrtn <- ua*sqrt(par1)/(c - par2)
samplesize <- sqrtn * sqrtn
ua
ub
c
sqrtn
samplesize
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,'population variance',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'null hypothesis about mean',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alternative hypothesis about mean',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'type I error',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'type II 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#ex4','sample size','example'),header=TRUE)
a<-table.element(a,samplesize)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')

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