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Description of Statistical Computation

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 computationSun, 07 Oct 2012 06:41:41 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/07/t1349606569svg9z49h5qwidq1.htm/, Retrieved Sat, 04 May 2024 14:36:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=172826, Retrieved Sat, 04 May 2024 14:36:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Testing Mean with unknown Variance - Critical Value] [post1-pre S] [2012-10-02 19:05:36] [ce03f21eb3e54b507ec8f2385bd7917e]
-   PD  [Testing Mean with unknown Variance - Critical Value] [I1M ≤ 20] [2012-10-02 19:20:44] [ce03f21eb3e54b507ec8f2385bd7917e]
- R  D    [Testing Mean with unknown Variance - Critical Value] [I1F ≤ 20] [2012-10-07 09:22:21] [74be16979710d4c4e7c6647856088456]
- RMPD      [Variability] [variability I1M] [2012-10-07 10:22:50] [ce03f21eb3e54b507ec8f2385bd7917e]
- RM D        [Testing Variance - Critical Value (Region)] [Variance I1M] [2012-10-07 10:31:47] [ce03f21eb3e54b507ec8f2385bd7917e]
- RM              [Minimum Sample Size - Testing Mean] [minimum sample size] [2012-10-07 10:41:41] [04b4f93d77ad48b80a96306d43249fd5] [Current]
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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172826&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172826&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ yule.wessa.net






Minimum Sample Size
Population Size105
Margin of Error1
Confidence0.95
Power0.5
Population Variance13.03
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)34.1158605076111
Minimum Sample Size (1 sided test)26.5817119261086

\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 & 13.03 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 34.1158605076111 \tabularnewline
Minimum Sample Size (1 sided test) & 26.5817119261086 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172826&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]13.03[/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]34.1158605076111[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]26.5817119261086[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172826&T=1

As an alternative you can also use a QR Code:  
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 Variance13.03
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)34.1158605076111
Minimum Sample Size (1 sided test)26.5817119261086






Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.5
Population Variance13.03
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)50.0542084336444
Minimum Sample Size (1 sided test)35.2532312068632

\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 & 13.03 \tabularnewline
z(alpha/2) + z(beta) & 1.95996398454005 \tabularnewline
z(alpha) + z(beta) & 1.64485362695147 \tabularnewline
Minimum Sample Size (2 sided test) & 50.0542084336444 \tabularnewline
Minimum Sample Size (1 sided test) & 35.2532312068632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172826&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]13.03[/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]50.0542084336444[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]35.2532312068632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172826&T=2

As an alternative you can also use a QR Code:  
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 Variance13.03
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)50.0542084336444
Minimum Sample Size (1 sided test)35.2532312068632






Minimum Sample Size (Unknown Population Variance)
Population Size105
Margin of Error1
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.0342449237467
t(alpha) + t(beta)1.70664831715316
Minimum Sample Size (2 sided test)35.8511189577839
Minimum Sample Size (1 sided test)28.0724847744385

\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) & 2.0342449237467 \tabularnewline
t(alpha) + t(beta) & 1.70664831715316 \tabularnewline
Minimum Sample Size (2 sided test) & 35.8511189577839 \tabularnewline
Minimum Sample Size (1 sided test) & 28.0724847744385 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172826&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]2.0342449237467[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]1.70664831715316[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]35.8511189577839[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]28.0724847744385[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172826&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172826&T=3

As an alternative you can also use a QR Code:  
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)2.0342449237467
t(alpha) + t(beta)1.70664831715316
Minimum Sample Size (2 sided test)35.8511189577839
Minimum Sample Size (1 sided test)28.0724847744385






Minimum Sample Size(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)2.00951906663022
t(alpha) + t(beta)1.69057427063159
Minimum Sample Size (2 sided test)52.6173144353295
Minimum Sample Size (1 sided test)37.2402789797155

\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) & 2.00951906663022 \tabularnewline
t(alpha) + t(beta) & 1.69057427063159 \tabularnewline
Minimum Sample Size (2 sided test) & 52.6173144353295 \tabularnewline
Minimum Sample Size (1 sided test) & 37.2402789797155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172826&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]2.00951906663022[/C][/ROW]
[ROW][C]t(alpha) + t(beta)[/C][C]1.69057427063159[/C][/ROW]
[ROW][C]Minimum Sample Size (2 sided test)[/C][C]52.6173144353295[/C][/ROW]
[ROW][C]Minimum Sample Size (1 sided test)[/C][C]37.2402789797155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172826&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172826&T=4

As an alternative you can also use a QR Code:  
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)2.00951906663022
t(alpha) + t(beta)1.69057427063159
Minimum Sample Size (2 sided test)52.6173144353295
Minimum Sample Size (1 sided test)37.2402789797155


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.99205 ; par2 = 20 ;
Parameters (R input):
par1 = 105 ; par2 = 1 ; par3 = 0.95 ; par4 = 13.03 ; 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')