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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_hypothesismean6.wasp
Title produced by softwareTesting Sample Mean with known Variance - Confidence Interval
Date of computationWed, 05 Nov 2008 05:15:00 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/05/t12258873244eg2cpyanh57amv.htm/, Retrieved Sun, 17 May 2026 16:39:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21733, Retrieved Sun, 17 May 2026 16:39:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact439

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Testing Sample Mean with known Variance - Confidence Interval] [Q6] [2008-11-05 12:15:00] [b4fc5040f26b33db57f84cfb8d1d2b82] [Current]
F   P     [Testing Sample Mean with known Variance - Confidence Interval] [Q5] [2008-11-06 11:34:09] [c5a66f1c8528a963efc2b82a8519f117]
F           [Testing Sample Mean with known Variance - Confidence Interval] [] [2008-11-11 20:12:54] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RM        [Testing Population Mean with known Variance - Confidence Interval] [verbetering q5] [2008-11-19 12:53:34] [c5a66f1c8528a963efc2b82a8519f117]
-   P         [Testing Population Mean with known Variance - Confidence Interval] [verbetering q5] [2008-11-19 12:56:47] [c5a66f1c8528a963efc2b82a8519f117]
F         [Testing Sample Mean with known Variance - Confidence Interval] [] [2008-11-11 20:14:19] [d2d412c7f4d35ffbf5ee5ee89db327d4]
Feedback Forum
2008-11-19 15:46:32 [Gregory Van Overmeiren] [reply] 
Ook hier gebruiken we weer de one-sided confidence interval van de right-tail, omdat enkel de afwijking van het vetpercentage naar boven toe een economisch voordeel voor de producent kan betekenen.

De rechter staart is nauwkeuriger, omdat de volledige 5% (foutmarge) toegewezen wordt aan de rechterkant.
(bij de two-sided wordt de 5% verdeeld over de linkse en rechtse tail, wat maakt dat de resultaten voor de two-sided extremer zijn.)

Ook al gaan we uit van een nulhypothese van 15.2% i.p.v. 15%, dan nog ligt het gemiddelde van de steekproef 0.1546 lager dan 0.189276559191704 en dus binnen het 95%-betrouwbaarheidsinterval.
2008-11-23 10:33:05 [Liese Tormans] [reply] 
De conclusie van de student is verkeerd. Als je de nulhypothese verandert van 15% naar 15,2 %, kan je zien dat het gemiddelde van de steekproef (15.46%) lager ligt dan het rechter 1-zijdig betrouwbaarheidsinterval (18.66%). We zien dus dat deze waarde nog binnen het betrouwbaarheidsinterval valt.

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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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21733&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21733&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21733&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'Gwilym Jenkins' @ 72.249.127.135






Testing Sample Mean with known Variance
Population variance0.012
Sample size27
Null hypothesis (H0)0.152
Confidence interval0.95
Type of IntervalLeft tailRight tail
Two-sided confidence interval at 0.950.1106803311796960.193319668820304
Left one-sided confidence interval at 0.950.117323440808296+inf
Right one-sided confidence interval at 0.95-inf0.186676559191704
more information about confidence interval

\begin{tabular}{lllllllll}
\hline
Testing Sample Mean with known Variance \tabularnewline
Population variance & 0.012 \tabularnewline
Sample size & 27 \tabularnewline
Null hypothesis (H0) & 0.152 \tabularnewline
Confidence interval & 0.95 \tabularnewline
Type of Interval & Left tail & Right tail \tabularnewline
Two-sided confidence interval at  0.95 & 0.110680331179696 & 0.193319668820304 \tabularnewline
Left one-sided confidence interval at  0.95 & 0.117323440808296 & +inf \tabularnewline
Right one-sided confidence interval at  0.95 & -inf & 0.186676559191704 \tabularnewline
more information about confidence interval \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21733&T=1

[TABLE]
[ROW][C]Testing Sample Mean with known Variance[/C][/ROW]
[ROW][C]Population variance[/C][C]0.012[/C][/ROW]
[ROW][C]Sample size[/C][C]27[/C][/ROW]
[ROW][C]Null hypothesis (H0)[/C][C]0.152[/C][/ROW]
[ROW][C]Confidence interval[/C][C]0.95[/C][/ROW]
[ROW][C]Type of Interval[/C][C]Left tail[/C][C]Right tail[/C][/ROW]
[ROW][C]Two-sided confidence interval at  0.95[/C][C]0.110680331179696[/C][C]0.193319668820304[/C][/ROW]
[ROW][C]Left one-sided confidence interval at  0.95[/C][C]0.117323440808296[/C][C]+inf[/C][/ROW]
[ROW][C]Right one-sided confidence interval at  0.95[/C][C]-inf[/C][C]0.186676559191704[/C][/ROW]
[ROW][C]more information about confidence interval[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21733&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21733&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:

Testing Sample Mean with known Variance
Population variance0.012
Sample size27
Null hypothesis (H0)0.152
Confidence interval0.95
Type of IntervalLeft tailRight tail
Two-sided confidence interval at 0.950.1106803311796960.193319668820304
Left one-sided confidence interval at 0.950.117323440808296+inf
Right one-sided confidence interval at 0.95-inf0.186676559191704
more information about confidence interval


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.012 ; par2 = 27 ; par3 = 0.152 ; par4 = 0.95 ;
Parameters (R input):
par1 = 0.012 ; par2 = 27 ; par3 = 0.152 ; par4 = 0.95 ;
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)
sigma <- sqrt(par1)
sqrtn <- sqrt(par2)
ua <- par3 - abs(qnorm((1-par4)/2))* sigma / sqrtn
ub <- par3 + abs(qnorm((1-par4)/2))* sigma / sqrtn
ua
ub
ul <- par3 - qnorm(par4) * sigma / sqrtn
ul
ur <- par3 + qnorm(par4) * sigma / sqrtn
ur
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm','Testing Sample Mean with known Variance','learn more about Statistical Hypothesis Testing about the Mean when the Variance is known'),3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Population variance',header=TRUE)
a<-table.element(a,par1,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Sample size',header=TRUE)
a<-table.element(a,par2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Null hypothesis (H0)',header=TRUE)
a<-table.element(a,par3,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Confidence interval',header=TRUE)
a<-table.element(a,par4,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Type of Interval',header=TRUE)
a<-table.element(a,'Left tail',header=TRUE)
a<-table.element(a,'Right tail',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('Two-sided confidence interval at ',par4), header=TRUE)
a<-table.element(a,ua)
a<-table.element(a,ub)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('Left one-sided confidence interval at ',par4), header=TRUE)
a<-table.element(a,ul)
a<-table.element(a,'+inf')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('Right one-sided confidence interval at ',par4), header=TRUE)
a<-table.element(a,'-inf')
a<-table.element(a,ur)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, hyperlink('ht_mean_knownvar.htm#ex6', 'more information about confidence interval','example'),3,TRUE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')