FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationSun, 27 Oct 2013 13:08:57 -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/2013/Oct/27/t13828937743rrllqevsr1mkin.htm/, Retrieved Tue, 10 Feb 2026 21:31:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=219945, Retrieved Tue, 10 Feb 2026 21:31:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact283

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] [WS 4 question 4] [2013-10-27 17:03:09] [1601e79f56036968990446024a6397e5]
-   PD    [Testing Mean with unknown Variance - Critical Value] [WS 4 Question 5] [2013-10-27 17:08:57] [6b92c6b72208b98f35c650918bf39b5d] [Current]
- RM        [Testing Mean with unknown Variance - Critical Value] [WS 4 Question 8 F...] [2013-10-29 10:13:25] [74be16979710d4c4e7c6647856088456]
- R PD      [Testing Mean with unknown Variance - Critical Value] [WS 4 Question 8 F...] [2013-10-29 10:16:23] [74be16979710d4c4e7c6647856088456]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 


19


25



17
22



21

26
20

14


23




20

22


15
20
22

20
28




25
26

17
23

13




24



14
22



23

22
24
21



23
22




21
26
15
25



17
25





27




25

19
26

20


20

18








18


19






23


17
23

23
11
18
24


16
24




24


21
25
22
21



24
24
21




18

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 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=219945&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]0 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=219945&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219945&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 time0 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 size63
Sample standard deviation3.71225672258781
Confidence0.95
Null hypothesis20
Sample Mean21.1587301587302
2-sided Confidence Interval[ 20.223810410058 , 22.0936499074023 ]
Left-sided Confidence Interval[ 20.3777621085879 , +inf ]
Right-sided Confidence Interval[ -inf, 21.9396982088724 ]

\begin{tabular}{lllllllll}
\hline
Hypothesis Test about the Mean - Confidence Interval \tabularnewline
Sample size & 63 \tabularnewline
Sample standard deviation & 3.71225672258781 \tabularnewline
Confidence & 0.95 \tabularnewline
Null hypothesis & 20 \tabularnewline
Sample Mean & 21.1587301587302 \tabularnewline
2-sided Confidence Interval & [ 20.223810410058 , 22.0936499074023 ] \tabularnewline
Left-sided Confidence Interval & [ 20.3777621085879 , +inf ] \tabularnewline
Right-sided Confidence Interval & [ -inf,  21.9396982088724 ] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219945&T=1

[TABLE]
[ROW][C]Hypothesis Test about the Mean - Confidence Interval[/C][/ROW]
[ROW][C]Sample size[/C][C]63[/C][/ROW]
[ROW][C]Sample standard deviation[/C][C]3.71225672258781[/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]21.1587301587302[/C][/ROW]
[ROW][C]2-sided Confidence Interval[/C][C][ 20.223810410058 , 22.0936499074023 ][/C][/ROW]
[ROW][C]Left-sided Confidence Interval[/C][C][ 20.3777621085879 , +inf ][/C][/ROW]
[ROW][C]Right-sided Confidence Interval[/C][C][ -inf,  21.9396982088724 ][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219945&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219945&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 size63
Sample standard deviation3.71225672258781
Confidence0.95
Null hypothesis20
Sample Mean21.1587301587302
2-sided Confidence Interval[ 20.223810410058 , 22.0936499074023 ]
Left-sided Confidence Interval[ 20.3777621085879 , +inf ]
Right-sided Confidence Interval[ -inf, 21.9396982088724 ]


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')