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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 computationMon, 10 Nov 2008 11:28:54 -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/10/t1226341791evinfb83c36yxvs.htm/, Retrieved Sun, 19 May 2024 07:24:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23173, Retrieved Sun, 19 May 2024 07:24:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135

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] [2008-11-10 18:28:54] [63302faa1e3976bf98d1de42298c0b24] [Current]
Feedback Forum
2008-11-20 14:38:29 [Kim Huysmans] [reply] 
We moeten hier naar 1 staart kijken omdat je een sterk vermoeden hebt dat er goedkoop vlees geleverd werd (Q3).
Bij een rechts 1 zijdig betrouwbaarheidsinterval zou dit liggen tussen - inf en 0.186676559191704.
Bij een links 1 zijdig betrouwbaarheidsinterval zou dit liggen tussen 0.117323440808296 en + inf

Verder zien we hier ook dat het gemiddelde van de steekproeven nog steeds binnen het interval ligt.
Stel dat we nu de 2 zijdige methode zouden gebruiken zien we nog steeds dat dit gemiddelde ligt binnen het interval.

We kunnen hieruit dus concluderen dat we niet kunnen bewijzen dat er effectief fraude gepleegd is.
2008-11-23 17:10:33 [Chi-Kwong Man] [reply] 
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.

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.
  2008-11-24 17:51:03 [Thomas Beyers] [reply] 
akkoord met bovenstaande opmerkingen
2008-11-24 19:56:31 [Bart Haemels] [reply] 
Je kijkt hier naar het two sided interval, je had hier moeten kijken naar het right one sided interval omdat dit enkel in het voordeel is van de leverancier. je hebt ook de Null Hypthesis op 0.15 gezet, dit had 0.152 ( staat in de opgave)
moeten zijn.

Dus de 0.152 valt nog steeds in het betrouwbaarheidsinterval van 95%, want 0.1546 < 0.1846

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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'George Udny Yule' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23173&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23173&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23173&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' @ 72.249.76.132






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=23173&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=23173&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23173&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')