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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_hypothesismeanu.wasp
Title produced by softwareTesting Mean with unknown Variance - Critical Value
Date of computationMon, 08 Oct 2012 11:16:51 -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/08/t134971058971zio7med0dkvng.htm/, Retrieved Tue, 10 Feb 2026 06:27:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173800, Retrieved Tue, 10 Feb 2026 06:27:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact353

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] [] [2012-10-08 15:16:51] [1243027a8c443f5e4dc521447a752890] [Current]
- R PD    [Testing Mean with unknown Variance - Critical Value] [] [2012-10-08 15:51:34] [2a1ff7840cf6f76052608b20a5401ef9]
- RMPD    [Testing Variance - Confidence Intervals for Sample Variance] [] [2012-10-08 15:55:12] [2a1ff7840cf6f76052608b20a5401ef9]
-           [Testing Variance - Confidence Intervals for Sample Variance] [] [2012-10-08 16:02:10] [2a1ff7840cf6f76052608b20a5401ef9]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 


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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173800&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173800&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173800&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Hypothesis Test about the Mean - Confidence Interval
Sample size42
Sample standard deviation3.80666632087885
Confidence0.95
Null hypothesis20
Sample Mean21.4047619047619
2-sided Confidence Interval[ 20.2185211718619 , 22.5910026376619 ]
Left-sided Confidence Interval[ 20.4162707259002 , +inf ]
Right-sided Confidence Interval[ -inf, 22.3932530836237 ]

\begin{tabular}{lllllllll}
\hline
Hypothesis Test about the Mean - Confidence Interval \tabularnewline
Sample size & 42 \tabularnewline
Sample standard deviation & 3.80666632087885 \tabularnewline
Confidence & 0.95 \tabularnewline
Null hypothesis & 20 \tabularnewline
Sample Mean & 21.4047619047619 \tabularnewline
2-sided Confidence Interval & [ 20.2185211718619 , 22.5910026376619 ] \tabularnewline
Left-sided Confidence Interval & [ 20.4162707259002 , +inf ] \tabularnewline
Right-sided Confidence Interval & [ -inf,  22.3932530836237 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173800&T=1

[TABLE]
[ROW][C]Hypothesis Test about the Mean - Confidence Interval[/C][/ROW]
[ROW][C]Sample size[/C][C]42[/C][/ROW]
[ROW][C]Sample standard deviation[/C][C]3.80666632087885[/C][/ROW]
[ROW][C]Confidence[/C][C]0.95[/C][/ROW]
[ROW][C]Null hypothesis[/C][C]20[/C][/ROW]
[ROW][C]Sample Mean[/C][C]21.4047619047619[/C][/ROW]
[ROW][C]2-sided Confidence Interval[/C][C][ 20.2185211718619 , 22.5910026376619 ][/C][/ROW]
[ROW][C]Left-sided Confidence Interval[/C][C][ 20.4162707259002 , +inf ][/C][/ROW]
[ROW][C]Right-sided Confidence Interval[/C][C][ -inf,  22.3932530836237 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173800&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173800&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:

Hypothesis Test about the Mean - Confidence Interval
Sample size42
Sample standard deviation3.80666632087885
Confidence0.95
Null hypothesis20
Sample Mean21.4047619047619
2-sided Confidence Interval[ 20.2185211718619 , 22.5910026376619 ]
Left-sided Confidence Interval[ 20.4162707259002 , +inf ]
Right-sided Confidence Interval[ -inf, 22.3932530836237 ]


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.95 ; par2 = 20 ;
Parameters (R input):
par1 = 0.95 ; par2 = 20 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
len <- length(x)
df <- len - 1
sd <- sd(x)
mx <- mean(x)
load(file='createtable')
delta2 <- abs(qt((1-par1)/2,df)) * sd / sqrt(len)
delta1 <- abs(qt((1-par1),df)) * sd / sqrt(len)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Hypothesis Test about the Mean - Confidence Interval',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample size',header=TRUE)
a<-table.element(a,len)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample standard deviation',header=TRUE)
a<-table.element(a,sd)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Null hypothesis',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample Mean',header=TRUE)
a<-table.element(a,mx)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'2-sided Confidence Interval',header=TRUE)
dum <- paste('[',mx-delta2)
dum <- paste(dum,',')
dum <- paste(dum,mx+delta2)
dum <- paste(dum,']')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Left-sided Confidence Interval',header=TRUE)
dum <- paste('[',mx-delta1)
dum <- paste(dum,', +inf ]')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Right-sided Confidence Interval',header=TRUE)
dum <- paste('[ -inf, ',mx+delta1)
dum <- paste(dum,']')
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')