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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_samplenorm.wasp
Title produced by softwareMinimum Sample Size - Testing Mean
Date of computationTue, 26 Oct 2010 20:29:38 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/26/t12881249385g8k877m51kj50m.htm/, Retrieved Thu, 30 May 2024 09:40:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=89645, Retrieved Thu, 30 May 2024 09:40:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168
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] [Intrinsic motivat...] [2010-10-22 14:27:55] [6bc4f9343b7ea3ef5a59412d1f72bb2b]
- RMPD      [Population Mean Test] [Smallest possible...] [2010-10-22 14:53:43] [6bc4f9343b7ea3ef5a59412d1f72bb2b]
- RMPD        [Minimum Sample Size - Testing Mean] [Sample size max. ...] [2010-10-23 10:10:07] [6bc4f9343b7ea3ef5a59412d1f72bb2b]
-   P             [Minimum Sample Size - Testing Mean] [ws 4 question 11] [2010-10-26 20:29:38] [05a3d060fb1d372fa2d84e37f098db3c] [Current]
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Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89645&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89645&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Minimum Sample Size
Population Size105
Margin of Error1
Confidence0.95
Power0.05
Population Variance13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)64.9899212937402
Minimum Sample Size (1 sided test)60.3717860543336

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.05 \tabularnewline
Population Variance & 13 \tabularnewline
z(alpha/2) + z(beta) & 3.60481761149153 \tabularnewline
z(alpha) + z(beta) & 3.28970725390294 \tabularnewline
Minimum Sample Size (2 sided test) & 64.9899212937402 \tabularnewline
Minimum Sample Size (1 sided test) & 60.3717860543336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89645&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]105[/C][/ROW]
[ROW][C]Margin of Error[/C][C]1[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.05[/C][/ROW]
[ROW][C]Population Variance[/C][C]13[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]3.60481761149153[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]3.28970725390294[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]64.9899212937402[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]60.3717860543336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89645&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Minimum Sample Size
Population Size105
Margin of Error1
Confidence0.95
Power0.05
Population Variance13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)64.9899212937402
Minimum Sample Size (1 sided test)60.3717860543336







Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.05
Population Variance13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)168.931230157553
Minimum Sample Size (1 sided test)140.688259612961

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (for Infinite Populations) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.05 \tabularnewline
Population Variance & 13 \tabularnewline
z(alpha/2) + z(beta) & 3.60481761149153 \tabularnewline
z(alpha) + z(beta) & 3.28970725390294 \tabularnewline
Minimum Sample Size (2 sided test) & 168.931230157553 \tabularnewline
Minimum Sample Size (1 sided test) & 140.688259612961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89645&T=2

[TABLE]
[ROW][C]Minimum Sample Size (for Infinite Populations)[/C][/ROW]
[ROW][C]Population Size[/C][C]infinite[/C][/ROW]
[ROW][C]Margin of Error[/C][C]1[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.05[/C][/ROW]
[ROW][C]Population Variance[/C][C]13[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]3.60481761149153[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]3.28970725390294[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]168.931230157553[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]140.688259612961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89645&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89645&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.05
Population Variance13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)168.931230157553
Minimum Sample Size (1 sided test)140.688259612961







Minimum Sample Size (Unknown Population Variance)
Population Size105
Margin of Error1
Confidence0.95
Power0.05
Population Varianceunknown
t(alpha/2) + t(beta)3.66675260030667
t(alpha) + t(beta)3.34185224422168
Minimum Sample Size (2 sided test)65.8301666270624
Minimum Sample Size (1 sided test)61.1769076976371

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (Unknown Population Variance) \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.05 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 3.66675260030667 \tabularnewline
t(alpha) + t(beta) & 3.34185224422168 \tabularnewline
Minimum Sample Size (2 sided test) & 65.8301666270624 \tabularnewline
Minimum Sample Size (1 sided test) & 61.1769076976371 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89645&T=3

[TABLE]
[ROW][C]Minimum Sample Size (Unknown Population Variance)[/C][/ROW]
[ROW][C]Population Size[/C][C]105[/C][/ROW]
[ROW][C]Margin of Error[/C][C]1[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.05[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]3.66675260030667[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]3.34185224422168[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]65.8301666270624[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]61.1769076976371[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89645&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89645&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Minimum Sample Size (Unknown Population Variance)
Population Size105
Margin of Error1
Confidence0.95
Power0.05
Population Varianceunknown
t(alpha/2) + t(beta)3.66675260030667
t(alpha) + t(beta)3.34185224422168
Minimum Sample Size (2 sided test)65.8301666270624
Minimum Sample Size (1 sided test)61.1769076976371







Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.05
Population Varianceunknown
t(alpha/2) + t(beta)3.62816902032638
t(alpha) + t(beta)3.31167025401027
Minimum Sample Size (2 sided test)171.126935720729
Minimum Sample Size (1 sided test)142.573078326854

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size(Infinite Population, Unknown Population Variance) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.05 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 3.62816902032638 \tabularnewline
t(alpha) + t(beta) & 3.31167025401027 \tabularnewline
Minimum Sample Size (2 sided test) & 171.126935720729 \tabularnewline
Minimum Sample Size (1 sided test) & 142.573078326854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=89645&T=4

[TABLE]
[ROW][C]Minimum Sample Size(Infinite Population, Unknown Population Variance)[/C][/ROW]
[ROW][C]Population Size[/C][C]infinite[/C][/ROW]
[ROW][C]Margin of Error[/C][C]1[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.05[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]3.62816902032638[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]3.31167025401027[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]171.126935720729[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]142.573078326854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=89645&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=89645&T=4

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.05
Population Varianceunknown
t(alpha/2) + t(beta)3.62816902032638
t(alpha) + t(beta)3.31167025401027
Minimum Sample Size (2 sided test)171.126935720729
Minimum Sample Size (1 sided test)142.573078326854



Parameters (Session):
par1 = 13 ; par2 = 20 ; par3 = 21 ; par4 = 0.05 ; par5 = 0.15 ;
Parameters (R input):
par1 = 105 ; par2 = 1 ; par3 = 0.95 ; par4 = 13 ; 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)
(z <- abs(qnorm((1-par3)/2)) + abs(qnorm(1-par5)))
(z1 <- abs(qnorm(1-par3)) + abs(qnorm(1-par5)))
z2 <- z*z
z2one <- z1*z1
z24 <- z2 * par4
z24one <- z2one * par4
npop <- array(NA, 200)
ppop <- array(NA, 200)
for (i in 1:200)
{
ppop[i] <- i * 100
npop[i] <- ppop[i] * z24 / (z24 + (ppop[i] - 1) * par2*par2)
}
bitmap(file='pic1.png')
plot(ppop,npop, xlab='population size', ylab='sample size (2 sided test)', main = paste('Confidence',par3))
dumtext <- paste('Margin of error = ',par2)
dumtext <- paste(dumtext,' Population Var. = ')
dumtext <- paste(dumtext, par4)
mtext(dumtext)
grid()
dev.off()
par2sq <- par2 * par2
num <- par1 * z24
denom <- z24 + (par1 - 1) * par2sq
(n <- num/denom)
num1 <- par1 * z24one
denom1 <- z24one + (par1 - 1) * par2sq
(n1 <- num1/denom1)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Margin of Error',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Power',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Variance',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z(alpha/2) + z(beta)',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z(alpha) + z(beta)',header=TRUE)
a<-table.element(a,z1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (2 sided test)',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (1 sided test)',header=TRUE)
a<-table.element(a,n1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
(ni <- z24 / (par2sq))
(ni1 <- z24one / (par2sq))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (for Infinite Populations)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Size',header=TRUE)
a<-table.element(a,'infinite')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Margin of Error',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Power',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Variance',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z(alpha/2) + z(beta)',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z(alpha) + z(beta)',header=TRUE)
a<-table.element(a,z1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (2 sided test)',header=TRUE)
a<-table.element(a,ni)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (1 sided test)',header=TRUE)
a<-table.element(a,ni1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
(z <- abs(qt((1-par3)/2,n-1)) + abs(qt(1-par5,n-1)))
(z1 <- abs(qt(1-par3,n1-1)) + abs(qt(1-par5,n1-1)))
z2 <- z*z
z2one <- z1*z1
z24 <- z2 * par4
z24one <- z2one * par4
par2sq <- par2 * par2
num <- par1 * z24
denom <- z24 + (par1 - 1) * par2sq
(n <- num/denom)
num1 <- par1 * z24one
denom1 <- z24one + (par1 - 1) * par2sq
(n1 <- num1/denom1)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (Unknown Population Variance)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Margin of Error',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Power',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Variance',header=TRUE)
a<-table.element(a,'unknown')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t(alpha/2) + t(beta)',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t(alpha) + t(beta)',header=TRUE)
a<-table.element(a,z1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (2 sided test)',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (1 sided test)',header=TRUE)
a<-table.element(a,n1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
(z <- abs(qt((1-par3)/2,ni-1)) + abs(qt(1-par5,ni-1)))
(z1 <- abs(qt(1-par3,ni1-1)) + abs(qt(1-par5,ni1-1)))
z2 <- z*z
z2one <- z1*z1
z24 <- z2 * par4
z24one <- z2one * par4
(ni <- z24 / (par2sq))
(ni1 <- z24one / (par2sq))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size
(Infinite Population, Unknown Population Variance)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Size',header=TRUE)
a<-table.element(a,'infinite')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Margin of Error',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Power',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population Variance',header=TRUE)
a<-table.element(a,'unknown')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t(alpha/2) + t(beta)',header=TRUE)
a<-table.element(a,z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t(alpha) + t(beta)',header=TRUE)
a<-table.element(a,z1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (2 sided test)',header=TRUE)
a<-table.element(a,ni)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Minimum Sample Size (1 sided test)',header=TRUE)
a<-table.element(a,ni1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')