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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

Thu, 11 Nov 2010 13:38:01 +0000

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/2010/Nov/11/t1289482615s2lkp2ty0ihhzng.htm/, Retrieved Fri, 26 Apr 2024 03:04:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=93343, Retrieved Fri, 26 Apr 2024 03:04:56 +0000

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Original text written by user:

Question 11

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

145

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Minimum Sample Size - Testing Mean] [Minimum sample size] [2010-11-11 13:38:01] [a983146d598997d6f3fbd2f942b92d3f] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93343&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93343&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93343&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	'Gwilym Jenkins' @ 72.249.127.135

Minimum Sample Size
Population Size	105
Margin of Error	13
Confidence	0.95
Power	0.5
Population Variance	0.36
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	0.00826102179376561
Minimum Sample Size (1 sided test)	0.00581838162758587

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 13 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & 0.36 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 0.00826102179376561 \tabularnewline
Minimum Sample Size (1 sided test) & 0.00581838162758587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93343&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]13[/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]0.36[/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]0.00826102179376561[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]0.00581838162758587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93343&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93343&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	105
Margin of Error	13
Confidence	0.95
Power	0.5
Population Variance	0.36
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	0.00826102179376561
Minimum Sample Size (1 sided test)	0.00581838162758587

Minimum Sample Size (for Infinite Populations)
Population Size	infinite
Margin of Error	13
Confidence	0.95
Power	0.5
Population Variance	0.36
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	0.00818298920384547
Minimum Sample Size (1 sided test)	0.00576328783120916

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (for Infinite Populations) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 13 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & 0.36 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 0.00818298920384547 \tabularnewline
Minimum Sample Size (1 sided test) & 0.00576328783120916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93343&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]13[/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]0.36[/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]0.00818298920384547[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]0.00576328783120916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93343&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93343&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	13
Confidence	0.95
Power	0.5
Population Variance	0.36
z(alpha/2) + z(beta)	1.95996398454005
z(alpha) + z(beta)	1.64485362695147
Minimum Sample Size (2 sided test)	0.00818298920384547
Minimum Sample Size (1 sided test)	0.00576328783120916

Minimum Sample Size (Unknown Population Variance)
Population Size	105
Margin of Error	13
Confidence	0.95
Power	0.5
Population Variance	unknown
t(alpha/2) + t(beta)	NaN
t(alpha) + t(beta)	NaN
Minimum Sample Size (2 sided test)	NaN
Minimum Sample Size (1 sided test)	NaN

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (Unknown Population Variance) \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 13 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & NaN \tabularnewline
t(alpha) + t(beta) & NaN \tabularnewline
Minimum Sample Size (2 sided test) & NaN \tabularnewline
Minimum Sample Size (1 sided test) & NaN \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93343&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]13[/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]NaN[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]NaN[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]NaN[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]NaN[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93343&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93343&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	105
Margin of Error	13
Confidence	0.95
Power	0.5
Population Variance	unknown
t(alpha/2) + t(beta)	NaN
t(alpha) + t(beta)	NaN
Minimum Sample Size (2 sided test)	NaN
Minimum Sample Size (1 sided test)	NaN

Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Size	infinite
Margin of Error	13
Confidence	0.95
Power	0.5
Population Variance	unknown
t(alpha/2) + t(beta)	NaN
t(alpha) + t(beta)	NaN
Minimum Sample Size (2 sided test)	NaN
Minimum Sample Size (1 sided test)	NaN

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size(Infinite Population, Unknown Population Variance) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 13 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.5 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & NaN \tabularnewline
t(alpha) + t(beta) & NaN \tabularnewline
Minimum Sample Size (2 sided test) & NaN \tabularnewline
Minimum Sample Size (1 sided test) & NaN \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93343&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]13[/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]NaN[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]NaN[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]NaN[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]NaN[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93343&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93343&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	13
Confidence	0.95
Power	0.5
Population Variance	unknown
t(alpha/2) + t(beta)	NaN
t(alpha) + t(beta)	NaN
Minimum Sample Size (2 sided test)	NaN
Minimum Sample Size (1 sided test)	NaN

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 105 ; par2 = 13 ; par3 = 0.95 ; par4 = 0.36 ; par5 = 0.50 ;

Parameters (R input):

par1 = 105 ; par2 = 13 ; par3 = 0.95 ; 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