FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_hypothesismean6.wasp
Title produced by softwareTesting Sample Mean with known Variance - Confidence Interval
Date of computationWed, 12 Nov 2008 12:15:23 -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/12/t12265173864r2nkcom8ioausa.htm/, Retrieved Sun, 19 May 2024 10:09:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24396, Retrieved Sun, 19 May 2024 10:09:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136

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] [CASE Pork Quality Q6] [2008-11-12 19:15:23] [20dfa2578b2b18ce36fdb36ac12aedd7] [Current]
Feedback Forum
2008-11-15 16:48:28 [Philip Van Herck] [reply] 
De bedoeling van deze berekening is dat we gaan kijken of de sample mean tussen het 2-sided betrouwbaarheidsinterval ligt voor de nieuwe nulhypothese. Dit is inderdaad het geval.
2008-11-20 12:54:43 [Steven Vercammen] [reply] 
De conclusie is onjuist. Hier gebruiken we de one-sided confidence interval van de right-tail omdat er veronderstelt wordt dat het vetpercentage enkel te hoog en nooit te laag kan zijn (dit zou te veel kosten voor de leverancier). Het is ook zo dat de rechter staart nauwkeuriger is, 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.
2008-11-22 18:35:44 [Marlies Polfliet] [reply] 
De conclusie van de student klopt niet. Ook hier gebruiken we de right one-sided confidence interval om dezelfde redenen als bij Q5 (economisch voordeel voor de producent). Ook gebruiken we 15,2% (in plaats van 15%) als nieuwe nulhypothese.
Met de nieuwe nulhypothese is de sample mean/gemiddelde van de steekproef (15,46%) nog steeds kleiner dan 18,67% (kritische waarde) en valt dus binnen het 95%-betrouwbaarheidsinterval.
2008-11-23 23:29:11 [Peter Van Doninck] [reply] 
De berekende gegevens zijn niet volledig correct! Ook hier gebruiken we de one sided confidence interval van de right tail. Ook indien de null hypothese 15,2% bedraagt ipv 15%, is 0,1546 nog steeds lager dan 0,1892, en ligt dus binnen het 95% betrouwbaarheidsinterval.
2008-11-24 15:07:07 [Julian De Ruyter] [reply] 
Er werd een verkeerde berekening gemaakt, de student gaf als H0 0.15 ipv 0.152, dit is de correcte berekening:
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/24/t12275363831lkyb3q9rxr4i62.htm
we concluderen dan dat als we uit gaan van een 0-hypothese van 15,2% in plaats van een 0-hypothese van 15%, dan ligt het gemiddelde van de steekproef (0,1546) nog altijd lager dan 0.186676559191704. Dit ligt dan nog altijd binnen het 95%-betrouwbaarheidsinterval.

Post a new message

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24396&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24396&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24396&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 Ronald Aylmer Fisher' @ 193.190.124.24






Testing Sample Mean with known Variance
Population variance0.012
Sample size27
Null hypothesis (H0)0.15
Confidence interval0.95
Type of IntervalLeft tailRight tail
Two-sided confidence interval at 0.950.1086803311796960.191319668820304
Left one-sided confidence interval at 0.950.115323440808296+inf
Right one-sided confidence interval at 0.95-inf0.184676559191704
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) & 0.15 \tabularnewline
Confidence interval & 0.95 \tabularnewline
Type of Interval & Left tail & Right tail \tabularnewline
Two-sided confidence interval at  0.95 & 0.108680331179696 & 0.191319668820304 \tabularnewline
Left one-sided confidence interval at  0.95 & 0.115323440808296 & +inf \tabularnewline
Right one-sided confidence interval at  0.95 & -inf & 0.184676559191704 \tabularnewline
more information about confidence interval \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24396&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]0.15[/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]0.108680331179696[/C][C]0.191319668820304[/C][/ROW]
[ROW][C]Left one-sided confidence interval at  0.95[/C][C]0.115323440808296[/C][C]+inf[/C][/ROW]
[ROW][C]Right one-sided confidence interval at  0.95[/C][C]-inf[/C][C]0.184676559191704[/C][/ROW]
[ROW][C]more information about confidence interval[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24396&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24396&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)0.15
Confidence interval0.95
Type of IntervalLeft tailRight tail
Two-sided confidence interval at 0.950.1086803311796960.191319668820304
Left one-sided confidence interval at 0.950.115323440808296+inf
Right one-sided confidence interval at 0.95-inf0.184676559191704
more information about confidence interval


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.012 ; par2 = 27 ; par3 = 0.15 ; par4 = 0.95 ;
Parameters (R input):
par1 = 0.012 ; par2 = 27 ; par3 = 0.15 ; 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')