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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 computationFri, 22 Oct 2010 09:22:07 +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/22/t1287739256fcosjcw98gkfr4o.htm/, Retrieved Thu, 30 May 2024 16:05:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87347, Retrieved Thu, 30 May 2024 16:05:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact263
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: vraag 7] [2010-10-22 08:43:56] [1fd136673b2a4fecb5c545b9b4a05d64]
- RMPD        [Minimum Sample Size - Testing Mean] [WS4: vraag 11 B] [2010-10-22 09:22:07] [380f6bceef280be3d93cc6fafd18141e] [Current]
F   P           [Minimum Sample Size - Testing Mean] [Q11] [2010-10-25 19:45:28] [87116ee6ef949037dfa02b8eb1a3bf97]
-   P           [Minimum Sample Size - Testing Mean] [ws4.1.11 B] [2010-10-25 19:51:05] [e4076051fbfb461c886b1e223cd7862f]
- R P           [Minimum Sample Size - Testing Mean] [] [2011-10-24 13:12:21] [8f7c6937e89a5f5716ed1e29130ab1fa]
-   P           [Minimum Sample Size - Testing Mean] [] [2011-10-24 17:54:24] [1dc3906a3b5a6ec06dc921f387100c9e]
- R               [Minimum Sample Size - Testing Mean] [Taak 11] [2011-10-25 06:42:00] [54b1f171ce7a12209ffa11b565e1dcf5]
- R P             [Minimum Sample Size - Testing Mean] [] [2011-11-07 14:59:19] [46d7ccc24e5d35a2decd922dfb3b3a39]
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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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87347&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87347&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87347&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Minimum Sample Size
Population Size105
Margin of Error1
Confidence0.95
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)34.0627943128074
Minimum Sample Size (1 sided test)26.5359777294951

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 1 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & 13 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 34.0627943128074 \tabularnewline
Minimum Sample Size (1 sided test) & 26.5359777294951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87347&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]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]13[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]1.95996398454005[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]1.64485362695147[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]34.0627943128074[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]26.5359777294951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87347&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87347&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
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)34.0627943128074
Minimum Sample Size (1 sided test)26.5359777294951







Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)49.9389646690236
Minimum Sample Size (1 sided test)35.1720649032404

\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 & 0.5 \tabularnewline
Population Variance & 13 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 49.9389646690236 \tabularnewline
Minimum Sample Size (1 sided test) & 35.1720649032404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87347&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]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]13[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]1.95996398454005[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]1.64485362695147[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]49.9389646690236[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]35.1720649032404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87347&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87347&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
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)49.9389646690236
Minimum Sample Size (1 sided test)35.1720649032404







Minimum Sample Size (Unknown Population Variance)
Population Size105
Margin of Error1
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.0343685160221
t(alpha) + t(beta)1.70676309978817
Minimum Sample Size (2 sided test)35.799583472935
Minimum Sample Size (1 sided test)28.0278658796924

\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 & 0.5 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 2.0343685160221 \tabularnewline
t(alpha) + t(beta) & 1.70676309978817 \tabularnewline
Minimum Sample Size (2 sided test) & 35.799583472935 \tabularnewline
Minimum Sample Size (1 sided test) & 28.0278658796924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87347&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]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]2.0343685160221[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]1.70676309978817[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]35.799583472935[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]28.0278658796924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87347&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87347&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
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.0343685160221
t(alpha) + t(beta)1.70676309978817
Minimum Sample Size (2 sided test)35.799583472935
Minimum Sample Size (1 sided test)28.0278658796924







Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.00963863419992
t(alpha) + t(beta)1.6906858682228
Minimum Sample Size (2 sided test)52.5024167208958
Minimum Sample Size (1 sided test)37.1594431651079

\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 & 0.5 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 2.00963863419992 \tabularnewline
t(alpha) + t(beta) & 1.6906858682228 \tabularnewline
Minimum Sample Size (2 sided test) & 52.5024167208958 \tabularnewline
Minimum Sample Size (1 sided test) & 37.1594431651079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87347&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]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]2.00963863419992[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]1.6906858682228[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]52.5024167208958[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]37.1594431651079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87347&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87347&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
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.00963863419992
t(alpha) + t(beta)1.6906858682228
Minimum Sample Size (2 sided test)52.5024167208958
Minimum Sample Size (1 sided test)37.1594431651079



Parameters (Session):
par1 = 0.95 ; par2 = 100 ;
Parameters (R input):
par1 = 105 ; par2 = 1 ; par3 = 0.95 ; par4 = 13 ; par5 = 0.50 ;
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')