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Author's title

Author

*Unverified author*

R Software Module

rwasp_samplenorm.wasp

Title produced by software

Minimum Sample Size - Testing Mean

Date of computation

Thu, 11 Nov 2010 20:03:13 +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/t1289506776d4qh221vmpl0n6g.htm/, Retrieved Fri, 19 Apr 2024 02:36:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=93799, Retrieved Fri, 19 Apr 2024 02:36:40 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

128

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

-     [One Sample Tests about the Mean] [] [2010-11-11 14:03:41] [f1052bedf858e5044a431fba108f61db]
- RM D    [Minimum Sample Size - Testing Mean] [] [2010-11-11 20:03:13] [d41d8cd98f00b204e9800998ecf8427e] [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	'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=93799&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=93799&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93799&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Minimum Sample Size
Population Size	105
Margin of Error	0.05
Confidence	0.95
Power	0.95
Population Variance	0.13
z(alpha/2) + z(beta)	3.60481761149153
z(alpha) + z(beta)	3.28970725390294
Minimum Sample Size (2 sided test)	90.995060936139
Minimum Sample Size (1 sided test)	88.622121879856

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Population Variance & 0.13 \tabularnewline
z(alpha/2) + z(beta) & 3.60481761149153 \tabularnewline
z(alpha) + z(beta) & 3.28970725390294 \tabularnewline
Minimum Sample Size (2 sided test) & 90.995060936139 \tabularnewline
Minimum Sample Size (1 sided test) & 88.622121879856 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93799&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]0.05[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Population Variance[/C][C]0.13[/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]90.995060936139[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]88.622121879856[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93799&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93799&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	0.05
Confidence	0.95
Power	0.95
Population Variance	0.13
z(alpha/2) + z(beta)	3.60481761149153
z(alpha) + z(beta)	3.28970725390294
Minimum Sample Size (2 sided test)	90.995060936139
Minimum Sample Size (1 sided test)	88.622121879856

Minimum Sample Size (for Infinite Populations)
Population Size	infinite
Margin of Error	0.05
Confidence	0.95
Power	0.95
Population Variance	0.13
z(alpha/2) + z(beta)	3.60481761149153
z(alpha) + z(beta)	3.28970725390294
Minimum Sample Size (2 sided test)	675.724920630212
Minimum Sample Size (1 sided test)	562.753038451846

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (for Infinite Populations) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Population Variance & 0.13 \tabularnewline
z(alpha/2) + z(beta) & 3.60481761149153 \tabularnewline
z(alpha) + z(beta) & 3.28970725390294 \tabularnewline
Minimum Sample Size (2 sided test) & 675.724920630212 \tabularnewline
Minimum Sample Size (1 sided test) & 562.753038451846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93799&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]0.05[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Population Variance[/C][C]0.13[/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]675.724920630212[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]562.753038451846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93799&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93799&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	0.05
Confidence	0.95
Power	0.95
Population Variance	0.13
z(alpha/2) + z(beta)	3.60481761149153
z(alpha) + z(beta)	3.28970725390294
Minimum Sample Size (2 sided test)	675.724920630212
Minimum Sample Size (1 sided test)	562.753038451846

Minimum Sample Size (Unknown Population Variance)
Population Size	105
Margin of Error	0.05
Confidence	0.95
Power	0.95
Population Variance	unknown
t(alpha/2) + t(beta)	3.64863805881815
t(alpha) + t(beta)	3.32486061624796
Minimum Sample Size (2 sided test)	91.2857677403267
Minimum Sample Size (1 sided test)	88.9138371404494

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size (Unknown Population Variance) \tabularnewline
Population Size & 105 \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 3.64863805881815 \tabularnewline
t(alpha) + t(beta) & 3.32486061624796 \tabularnewline
Minimum Sample Size (2 sided test) & 91.2857677403267 \tabularnewline
Minimum Sample Size (1 sided test) & 88.9138371404494 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93799&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]0.05[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]3.64863805881815[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]3.32486061624796[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]91.2857677403267[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]88.9138371404494[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93799&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93799&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	0.05
Confidence	0.95
Power	0.95
Population Variance	unknown
t(alpha/2) + t(beta)	3.64863805881815
t(alpha) + t(beta)	3.32486061624796
Minimum Sample Size (2 sided test)	91.2857677403267
Minimum Sample Size (1 sided test)	88.9138371404494

Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Size	infinite
Margin of Error	0.05
Confidence	0.95
Power	0.95
Population Variance	unknown
t(alpha/2) + t(beta)	3.6106012072724
t(alpha) + t(beta)	3.29514131593062
Minimum Sample Size (2 sided test)	677.89493605376
Minimum Sample Size (1 sided test)	564.613727181554

\begin{tabular}{lllllllll}
\hline
Minimum Sample Size(Infinite Population, Unknown Population Variance) \tabularnewline
Population Size & infinite \tabularnewline
Margin of Error & 0.05 \tabularnewline
Confidence & 0.95 \tabularnewline
Power & 0.95 \tabularnewline
Population Variance & unknown \tabularnewline
t(alpha/2) + t(beta) & 3.6106012072724 \tabularnewline
t(alpha) + t(beta) & 3.29514131593062 \tabularnewline
Minimum Sample Size (2 sided test) & 677.89493605376 \tabularnewline
Minimum Sample Size (1 sided test) & 564.613727181554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93799&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]0.05[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Power[/C][C]0.95[/C][/ROW]
[ROW][C]Population Variance[/C][C]unknown[/C][/ROW]
[ROW][C]t(alpha/2) + t(beta)[/C][C]3.6106012072724[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]3.29514131593062[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]677.89493605376[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]564.613727181554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93799&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93799&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	0.05
Confidence	0.95
Power	0.95
Population Variance	unknown
t(alpha/2) + t(beta)	3.6106012072724
t(alpha) + t(beta)	3.29514131593062
Minimum Sample Size (2 sided test)	677.89493605376
Minimum Sample Size (1 sided test)	564.613727181554

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = two.sided ; par2 = 0.95 ; par3 = 20 ;

Parameters (R input):

par1 = 105 ; par2 = 0.05 ; par3 = 0.95 ; par4 = 0.13 ; par5 = 0.95 ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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