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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwareTesting Mean with unknown Variance - Critical Value
Date of computationTue, 25 Oct 2011 15:51:57 -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/2011/Oct/25/t1319572329hdancdd36qtpxpw.htm/, Retrieved Tue, 10 Feb 2026 20:08:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=136193, Retrieved Tue, 10 Feb 2026 20:08:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact380

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] [Question 2 - Exam...] [2010-10-26 09:16:47] [1429a1a14191a86916b95357f6de790b]
-   PD  [Testing Mean with unknown Variance - Critical Value] [] [2011-10-25 16:40:55] [e21b9c93af4eb9605ecfaf58a559e5ab]
- R P     [Testing Mean with unknown Variance - Critical Value] [] [2011-10-25 16:48:11] [e21b9c93af4eb9605ecfaf58a559e5ab]
-  M          [Testing Mean with unknown Variance - Critical Value] [] [2011-10-25 19:51:57] [3a7d19dd1b06a6e8757d1652762671da] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
26
20
19

20
25

22
26
22


19
24
26

13


22

21
7

17
25
25
19

23

22
21



18


22
18
23
20


15


21

18
19
22
16

18
20
24

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.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=136193&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]'George Udny Yule' @ yule.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=136193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136193&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'George Udny Yule' @ yule.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 size36
Sample standard deviation3.92428337406972
Confidence0.95
Null hypothesis20
Sample Mean20.5
2-sided Confidence Interval[ 19.1722135349333 , 21.8277864650667 ]
Left-sided Confidence Interval[ 19.3949398157745 , +inf ]
Right-sided Confidence Interval[ -inf, 21.6050601842255 ]

\begin{tabular}{lllllllll}
\hline
Hypothesis Test about the Mean - Confidence Interval \tabularnewline
Sample size & 36 \tabularnewline
Sample standard deviation & 3.92428337406972 \tabularnewline
Confidence & 0.95 \tabularnewline
Null hypothesis & 20 \tabularnewline
Sample Mean & 20.5 \tabularnewline
2-sided Confidence Interval & [ 19.1722135349333 , 21.8277864650667 ] \tabularnewline
Left-sided Confidence Interval & [ 19.3949398157745 , +inf ] \tabularnewline
Right-sided Confidence Interval & [ -inf,  21.6050601842255 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=136193&T=1

[TABLE]
[ROW][C]Hypothesis Test about the Mean - Confidence Interval[/C][/ROW]
[ROW][C]Sample size[/C][C]36[/C][/ROW]
[ROW][C]Sample standard deviation[/C][C]3.92428337406972[/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]20.5[/C][/ROW]
[ROW][C]2-sided Confidence Interval[/C][C][ 19.1722135349333 , 21.8277864650667 ][/C][/ROW]
[ROW][C]Left-sided Confidence Interval[/C][C][ 19.3949398157745 , +inf ][/C][/ROW]
[ROW][C]Right-sided Confidence Interval[/C][C][ -inf,  21.6050601842255 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=136193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=136193&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 size36
Sample standard deviation3.92428337406972
Confidence0.95
Null hypothesis20
Sample Mean20.5
2-sided Confidence Interval[ 19.1722135349333 , 21.8277864650667 ]
Left-sided Confidence Interval[ 19.3949398157745 , +inf ]
Right-sided Confidence Interval[ -inf, 21.6050601842255 ]


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.95 ; par2 = 20 ;
Parameters (R input):
par1 = 0.95 ; par2 = 20 ; par3 = ; par4 = ; par5 = ; 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)
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')