## Free Statistics

of Irreproducible Research!

Author's title
Author*Unverified author*
R Software Modulerwasp_hypothesisprop1.wasp
Title produced by softwareTesting Population Proportion - Critical Value
Date of computationSat, 02 May 2015 09:04:40 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/02/t1430553924rltuf5b43hmod9e.htm/, Retrieved Tue, 09 Aug 2022 20:54:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278999, Retrieved Tue, 09 Aug 2022 20:54:10 +0000
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Estimated Impact200
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-       [Testing Population Proportion - Critical Value] [NVNS] [2015-05-02 08:04:40] [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 1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278999&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278999&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278999&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' @ jenkins.wessa.net

 Testing Population Proportion (normal approximation) Sample size 15249 Sample Proportion 0.00085 Null hypothesis 0.00083 Type I error (alpha) 0.05 1-sided critical value 0.00121358826611326 1-sided test Do not reject the Null Hypothesis 2-sided Confidence Interval(sample proportion) [ 0.000392926389220692 , 0.00130707361077931 ] 2-sided test Do not reject the Null Hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (normal approximation) \tabularnewline
Sample size & 15249 \tabularnewline
Sample Proportion & 0.00085 \tabularnewline
Null hypothesis & 0.00083 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
1-sided critical value & 0.00121358826611326 \tabularnewline
1-sided test & Do not reject the Null Hypothesis \tabularnewline
2-sided Confidence Interval(sample proportion) & [ 0.000392926389220692 , 0.00130707361077931 ] \tabularnewline
2-sided test & Do not reject the Null Hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278999&T=1

[TABLE]
[ROW][C]Testing Population Proportion (normal approximation)[/C][/ROW]
[ROW][C]Sample size[/C][C]15249[/C][/ROW]
[ROW][C]Sample Proportion[/C][C]0.00085[/C][/ROW]
[ROW][C]Null hypothesis[/C][C]0.00083[/C][/ROW]
[ROW][C]Type I error (alpha)[/C][C]0.05[/C][/ROW]
[ROW][C]1-sided critical value[/C][C]0.00121358826611326[/C][/ROW]
[ROW][C]1-sided test[/C][C]Do not reject the Null Hypothesis[/C][/ROW]
[ROW][C]2-sided Confidence Interval(sample proportion)[/C][C][ 0.000392926389220692 , 0.00130707361077931 ][/C][/ROW]
[ROW][C]2-sided test[/C][C]Do not reject the Null Hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278999&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278999&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Testing Population Proportion (normal approximation) Sample size 15249 Sample Proportion 0.00085 Null hypothesis 0.00083 Type I error (alpha) 0.05 1-sided critical value 0.00121358826611326 1-sided test Do not reject the Null Hypothesis 2-sided Confidence Interval(sample proportion) [ 0.000392926389220692 , 0.00130707361077931 ] 2-sided test Do not reject the Null Hypothesis

 Testing Population Proportion (Agresti-Coull method) Sample size 15249 Sample Proportion 0.00085 Null hypothesis 0.00083 Type I error (alpha) 0.05 Left 1-sided confidence interval [ 0.000544902634820062 , 1 ] Right 1-sided confidence interval [ 0 , 0.0013321886434326 ] 2-sided Confidence Interval(sample proportion) [ 0.000501719921630758 , 0.00144970394264085 ]

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (Agresti-Coull method) \tabularnewline
Sample size & 15249 \tabularnewline
Sample Proportion & 0.00085 \tabularnewline
Null hypothesis & 0.00083 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
Left 1-sided confidence interval & [ 0.000544902634820062 , 1 ] \tabularnewline
Right 1-sided confidence interval & [ 0 , 0.0013321886434326  ] \tabularnewline
2-sided Confidence Interval(sample proportion) & [ 0.000501719921630758 , 0.00144970394264085 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278999&T=2

[TABLE]
[ROW][C]Testing Population Proportion (Agresti-Coull method)[/C][/ROW]
[ROW][C]Sample size[/C][C]15249[/C][/ROW]
[ROW][C]Sample Proportion[/C][C]0.00085[/C][/ROW]
[ROW][C]Null hypothesis[/C][C]0.00083[/C][/ROW]
[ROW][C]Type I error (alpha)[/C][C]0.05[/C][/ROW]
[ROW][C]Left 1-sided confidence interval[/C][C][ 0.000544902634820062 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval[/C][C][ 0 , 0.0013321886434326  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(sample proportion)[/C][C][ 0.000501719921630758 , 0.00144970394264085 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278999&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278999&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Testing Population Proportion (Agresti-Coull method) Sample size 15249 Sample Proportion 0.00085 Null hypothesis 0.00083 Type I error (alpha) 0.05 Left 1-sided confidence interval [ 0.000544902634820062 , 1 ] Right 1-sided confidence interval [ 0 , 0.0013321886434326 ] 2-sided Confidence Interval(sample proportion) [ 0.000501719921630758 , 0.00144970394264085 ]

 Testing Population Proportion (Exact and Wilson method) Sample size 15249 Sample Proportion 0.00085 Null hypothesis 0.00083 Type I error (alpha) 0.05 Left 1-sided confidence interval(Exact method) [ 0.000502402433655345 , 1 ] Right 1-sided confidence interval(Exact method) [ 0 , 0.00135199206960017 ] 2-sided Confidence Interval(Exact method) [ 0.000452175896555022 , 0.00145420777505683 ] Left 1-sided confidence interval(Wilson method) [ 0.000540429973704393 , 1 ] Right 1-sided confidence interval(Wilson method) [ 0 , 0.00133666130454827 ] 2-sided Confidence Interval(Wilson method) [ 0.00049644610027278 , 0.00145497776399883 ]

\begin{tabular}{lllllllll}
\hline
Testing Population Proportion (Exact and Wilson method) \tabularnewline
Sample size & 15249 \tabularnewline
Sample Proportion & 0.00085 \tabularnewline
Null hypothesis & 0.00083 \tabularnewline
Type I error (alpha) & 0.05 \tabularnewline
Left 1-sided confidence interval(Exact method) & [ 0.000502402433655345 , 1 ] \tabularnewline
Right 1-sided confidence interval(Exact method) & [ 0 , 0.00135199206960017  ] \tabularnewline
2-sided Confidence Interval(Exact method) & [ 0.000452175896555022 , 0.00145420777505683 ] \tabularnewline
Left 1-sided confidence interval(Wilson method) & [ 0.000540429973704393 , 1 ] \tabularnewline
Right 1-sided confidence interval(Wilson method) & [ 0 , 0.00133666130454827  ] \tabularnewline
2-sided Confidence Interval(Wilson method) & [ 0.00049644610027278 , 0.00145497776399883 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278999&T=3

[TABLE]
[ROW][C]Testing Population Proportion (Exact and Wilson method)[/C][/ROW]
[ROW][C]Sample size[/C][C]15249[/C][/ROW]
[ROW][C]Sample Proportion[/C][C]0.00085[/C][/ROW]
[ROW][C]Null hypothesis[/C][C]0.00083[/C][/ROW]
[ROW][C]Type I error (alpha)[/C][C]0.05[/C][/ROW]
[ROW][C]Left 1-sided confidence interval(Exact method)[/C][C][ 0.000502402433655345 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval(Exact method)[/C][C][ 0 , 0.00135199206960017  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(Exact method)[/C][C][ 0.000452175896555022 , 0.00145420777505683 ][/C][/ROW]
[ROW][C]Left 1-sided confidence interval(Wilson method)[/C][C][ 0.000540429973704393 , 1 ][/C][/ROW]
[ROW][C]Right 1-sided confidence interval(Wilson method)[/C][C][ 0 , 0.00133666130454827  ][/C][/ROW]
[ROW][C]2-sided Confidence Interval(Wilson method)[/C][C][ 0.00049644610027278 , 0.00145497776399883 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278999&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278999&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Testing Population Proportion (Exact and Wilson method) Sample size 15249 Sample Proportion 0.00085 Null hypothesis 0.00083 Type I error (alpha) 0.05 Left 1-sided confidence interval(Exact method) [ 0.000502402433655345 , 1 ] Right 1-sided confidence interval(Exact method) [ 0 , 0.00135199206960017 ] 2-sided Confidence Interval(Exact method) [ 0.000452175896555022 , 0.00145420777505683 ] Left 1-sided confidence interval(Wilson method) [ 0.000540429973704393 , 1 ] Right 1-sided confidence interval(Wilson method) [ 0 , 0.00133666130454827 ] 2-sided Confidence Interval(Wilson method) [ 0.00049644610027278 , 0.00145497776399883 ]

Parameters (Session):
par1 = 15249 ; par2 = 0.00085 ; par3 = 0.00083 ; par4 = 0.05 ;
Parameters (R input):
par1 = 15249 ; par2 = 0.00085 ; par3 = 0.00083 ; par4 = 0.05 ;
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)if (par2 < par3){ucv <- qnorm(par4)} else {ucv <- -qnorm(par4)}cv1 <- par3 + ucv * sqrt(par3 * (1-par3) / par1)cv2low <- par2 - abs(qnorm(par4/2)) * sqrt(par3 * (1-par3) / par1)cv2upp <- par2 + abs(qnorm(par4/2)) * sqrt(par3 * (1-par3) / par1)z21 <- qnorm(par4/2)^2 / par1z2 <- qnorm(par4/2)^2 / (2*par1)z24 <- qnorm(par4/2)^2 / (4*par1^2)cv2lowexact <- (par2 + z2 - abs(qnorm(par4/2)) * sqrt(par3 * (1-par3) / par1 + z24)) / (1 + z21)cv2uppexact <- (par2 + z2 + abs(qnorm(par4/2)) * sqrt(par3 * (1-par3) / par1 + z24)) / (1 + z21)z11 <- qnorm(par4)^2 / par1z1 <- qnorm(par4)^2 / (2*par1)z14 <- qnorm(par4)^2 / (4*par1^2)cv1lowexact <- (par2 + z1 - abs(qnorm(par4)) * sqrt(par3 * (1-par3) / par1 + z14)) / (1 + z11)cv1uppexact <- (par2 + z1 + abs(qnorm(par4)) * sqrt(par3 * (1-par3) / par1 + z14)) / (1 + z11)load(file='createtable')a<-table.start()a<-table.row.start(a)a<-table.element(a,'Testing Population Proportion (normal approximation)',2,TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Sample size',header=TRUE)a<-table.element(a,par1)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Sample Proportion',header=TRUE)a<-table.element(a,par2)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Null hypothesis',header=TRUE)a<-table.element(a,par3)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Type I error (alpha)',header=TRUE)a<-table.element(a,par4)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'1-sided critical value',header=TRUE)a<-table.element(a,cv1)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'1-sided test',header=TRUE)if (par2 < par3){if (par2 < cv1){a<-table.element(a,'Reject the Null Hypothesis')} else {a<-table.element(a,'Do not reject the Null Hypothesis')}} else {if (par2 > cv1){a<-table.element(a,'Reject the Null Hypothesis')} else {a<-table.element(a,'Do not reject the Null Hypothesis')}}a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'2-sided Confidence Interval(sample proportion)',header=TRUE)dum <- paste('[',cv2low)dum <- paste(dum,',')dum <- paste(dum,cv2upp)dum <- paste(dum,']')a<-table.element(a,dum)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'2-sided test',header=TRUE)if ((par3 < cv2low) | (par3 > cv2upp)){a<-table.element(a,'Reject the Null Hypothesis')} else {a<-table.element(a,'Do not reject the Null Hypothesis')}a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable.tab')a<-table.start()a<-table.row.start(a)a<-table.element(a,'Testing Population Proportion (Agresti-Coull method)',2,TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Sample size',header=TRUE)a<-table.element(a,par1)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Sample Proportion',header=TRUE)a<-table.element(a,par2)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Null hypothesis',header=TRUE)a<-table.element(a,par3)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Type I error (alpha)',header=TRUE)a<-table.element(a,par4)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Left 1-sided confidence interval',header=TRUE)dum <- paste('[',cv1lowexact)dum <- paste(dum,', 1 ]')a<-table.element(a,dum)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Right 1-sided confidence interval',header=TRUE)dum <- paste('[ 0 ,',cv1uppexact)dum <- paste(dum,' ]')a<-table.element(a,dum)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'2-sided Confidence Interval(sample proportion)',header=TRUE)dum <- paste('[',cv2lowexact)dum <- paste(dum,',')dum <- paste(dum,cv2uppexact)dum <- paste(dum,']')a<-table.element(a,dum)a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable.tab')library(Hmisc)re <- binconf(par2*par1,par1,par4,method='exact')re1 <- binconf(par2*par1,par1,par4*2,method='exact')rw <- binconf(par2*par1,par1,par4,method='wilson')rw1 <- binconf(par2*par1,par1,par4*2,method='wilson')a<-table.start()a<-table.row.start(a)a<-table.element(a,'Testing Population Proportion (Exact and Wilson method)',2,TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Sample size',header=TRUE)a<-table.element(a,par1)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Sample Proportion',header=TRUE)a<-table.element(a,par2)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Null hypothesis',header=TRUE)a<-table.element(a,par3)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Type I error (alpha)',header=TRUE)a<-table.element(a,par4)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Left 1-sided confidence interval(Exact method)',header=TRUE)dum <- paste('[',re1[2])dum <- paste(dum,', 1 ]')a<-table.element(a,dum)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Right 1-sided confidence interval(Exact method)',header=TRUE)dum <- paste('[ 0 ,',re1[3])dum <- paste(dum,' ]')a<-table.element(a,dum)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'2-sided Confidence Interval(Exact method)',header=TRUE)dum <- paste('[',re[2])dum <- paste(dum,',')dum <- paste(dum,re[3])dum <- paste(dum,']')a<-table.element(a,dum)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Left 1-sided confidence interval(Wilson method)',header=TRUE)dum <- paste('[',rw1[2])dum <- paste(dum,', 1 ]')a<-table.element(a,dum)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Right 1-sided confidence interval(Wilson method)',header=TRUE)dum <- paste('[ 0 ,',rw1[3])dum <- paste(dum,' ]')a<-table.element(a,dum)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'2-sided Confidence Interval(Wilson method)',header=TRUE)dum <- paste('[',rw[2])dum <- paste(dum,',')dum <- paste(dum,rw[3])dum <- paste(dum,']')a<-table.element(a,dum)a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable.tab')