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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_samplenorm.wasp

Title produced by software

Minimum Sample Size - Testing Mean

Date of computation

Wed, 30 Oct 2013 14:24:05 -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/30/t1383157465tdeg0red0ksekbp.htm/, Retrieved Thu, 02 May 2024 12:21:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=221264, Retrieved Thu, 02 May 2024 12:21:55 +0000

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-     [Minimum Sample Size - Testing Mean] [WS4: V9] [2013-10-30 17:48:48] [fff8fef6abdb3da482127903f3b009ef]
- R P     [Minimum Sample Size - Testing Mean] [WS4: V10] [2013-10-30 18:24:05] [0af71617a8b1f082fed242286206dd2f] [Current]

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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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=221264&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=221264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=221264&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Minimum Sample Size
Population Size	98
Margin of Error	0.15
Confidence	0.85
Power	0.5
Population Variance	0.36
z(alpha/2) + z(beta)	1.43953147093846
z(alpha) + z(beta)	1.03643338949379
Minimum Sample Size (2 sided test)	24.9645732819499
Minimum Sample Size (1 sided test)	14.7506711404159

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 98 \tabularnewline
Margin of Error & 0.15 \tabularnewline
Confidence & 0.85 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & 0.36 \tabularnewline
z(alpha/2) + z(beta) & 1.43953147093846 \tabularnewline
z(alpha) + z(beta) & 1.03643338949379 \tabularnewline
Minimum Sample Size (2 sided test) & 24.9645732819499 \tabularnewline
Minimum Sample Size (1 sided test) & 14.7506711404159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=221264&T=1

[TABLE]
[ROW][C]Minimum Sample Size[/C][/ROW]
[ROW][C]Population Size[/C][C]98[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.15[/C][/ROW]
[ROW][C]Confidence[/C][C]0.85[/C][/ROW]
[ROW][C]Power[/C][C]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]0.36[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]1.43953147093846[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]1.03643338949379[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]24.9645732819499[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]14.7506711404159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=221264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=221264&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 Size	98
Margin of Error	0.15
Confidence	0.85
Power	0.5
Population Variance	0.36
z(alpha/2) + z(beta)	1.43953147093846
z(alpha) + z(beta)	1.03643338949379
Minimum Sample Size (2 sided test)	24.9645732819499
Minimum Sample Size (1 sided test)	14.7506711404159

Minimum Sample Size (for Infinite Populations)
Population Size	infinite
Margin of Error	0.15
Confidence	0.85
Power	0.5
Population Variance	0.36
z(alpha/2) + z(beta)	1.43953147093846
z(alpha) + z(beta)	1.03643338949379
Minimum Sample Size (2 sided test)	33.1560136931557
Minimum Sample Size (1 sided test)	17.1871067337214

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (for Infinite Populations) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.15 \tabularnewline
Confidence & 0.85 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & 0.36 \tabularnewline
z(alpha/2) + z(beta) & 1.43953147093846 \tabularnewline
z(alpha) + z(beta) & 1.03643338949379 \tabularnewline
Minimum Sample Size (2 sided test) & 33.1560136931557 \tabularnewline
Minimum Sample Size (1 sided test) & 17.1871067337214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=221264&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]0.15[/C][/ROW]
[ROW][C]Confidence[/C][C]0.85[/C][/ROW]
[ROW][C]Power[/C][C]0.5[/C][/ROW]
[ROW][C]Population Variance[/C][C]0.36[/C][/ROW]
[ROW][C]z(alpha/2) + z(beta)[/C][C]1.43953147093846[/C][/ROW]
[ROW][C]z(alpha) + z(beta)[/C][C]1.03643338949379[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]33.1560136931557[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]17.1871067337214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=221264&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=221264&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 Size	infinite
Margin of Error	0.15
Confidence	0.85
Power	0.5
Population Variance	0.36
z(alpha/2) + z(beta)	1.43953147093846
z(alpha) + z(beta)	1.03643338949379
Minimum Sample Size (2 sided test)	33.1560136931557
Minimum Sample Size (1 sided test)	17.1871067337214

Minimum Sample Size (Unknown Population Variance)
Population Size	98
Margin of Error	0.15
Confidence	0.85
Power	0.5
Population Variance	unknown
t(alpha/2) + t(beta)	1.48720848220913
t(alpha) + t(beta)	1.07703020978183
Minimum Sample Size (2 sided test)	26.1962480394743
Minimum Sample Size (1 sided test)	15.7396348113451

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (Unknown Population Variance) \tabularnewline
Population Size & 98 \tabularnewline
Margin of Error & 0.15 \tabularnewline
Confidence & 0.85 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 1.48720848220913 \tabularnewline
t(alpha) + t(beta) & 1.07703020978183 \tabularnewline
Minimum Sample Size (2 sided test) & 26.1962480394743 \tabularnewline
Minimum Sample Size (1 sided test) & 15.7396348113451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=221264&T=3

[TABLE]
[ROW][C]Minimum Sample Size (Unknown Population Variance)[/C][/ROW]
[ROW][C]Population Size[/C][C]98[/C][/ROW]
[ROW][C]Margin of Error[/C][C]0.15[/C][/ROW]
[ROW][C]Confidence[/C][C]0.85[/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]1.48720848220913[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]1.07703020978183[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]26.1962480394743[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]15.7396348113451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=221264&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=221264&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 Size	98
Margin of Error	0.15
Confidence	0.85
Power	0.5
Population Variance	unknown
t(alpha/2) + t(beta)	1.48720848220913
t(alpha) + t(beta)	1.07703020978183
Minimum Sample Size (2 sided test)	26.1962480394743
Minimum Sample Size (1 sided test)	15.7396348113451

Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Size	infinite
Margin of Error	0.15
Confidence	0.85
Power	0.5
Population Variance	unknown
t(alpha/2) + t(beta)	1.47476575079602
t(alpha) + t(beta)	1.07072308204556
Minimum Sample Size (2 sided test)	34.7989443155354
Minimum Sample Size (1 sided test)	18.3431666948022

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size(Infinite Population, Unknown Population Variance) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.15 \tabularnewline
Confidence & 0.85 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 1.47476575079602 \tabularnewline
t(alpha) + t(beta) & 1.07072308204556 \tabularnewline
Minimum Sample Size (2 sided test) & 34.7989443155354 \tabularnewline
Minimum Sample Size (1 sided test) & 18.3431666948022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=221264&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]0.15[/C][/ROW]
[ROW][C]Confidence[/C][C]0.85[/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]1.47476575079602[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]1.07072308204556[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]34.7989443155354[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]18.3431666948022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=221264&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=221264&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 Size	infinite
Margin of Error	0.15
Confidence	0.85
Power	0.5
Population Variance	unknown
t(alpha/2) + t(beta)	1.47476575079602
t(alpha) + t(beta)	1.07072308204556
Minimum Sample Size (2 sided test)	34.7989443155354
Minimum Sample Size (1 sided test)	18.3431666948022

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 98 ; par2 = 0.15 ; par3 = 0.85 ; par4 = 0.36 ; par5 = 0.50 ;

Parameters (R input):

par1 = 98 ; par2 = 0.15 ; par3 = 0.85 ; par4 = 0.36 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code