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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 computationThu, 13 Nov 2008 08:02:49 -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/13/t12265885926v55s4am0aptpn2.htm/, Retrieved Sun, 19 May 2024 12:19:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24641, Retrieved Sun, 19 May 2024 12:19:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Box-Cox Linearity Plot] [question 3 box-co...] [2008-11-12 15:13:33] [31c9f333c18b3396ccf9d2485dd39c8a]
F RMPD  [Maximum-likelihood Fitting - Normal Distribution] [question 5] [2008-11-12 15:49:20] [31c9f333c18b3396ccf9d2485dd39c8a]
F RMPD      [Testing Sample Mean with known Variance - Confidence Interval] [question 6] [2008-11-13 15:02:49] [490fee4f334e2e025c95681783e3fd0b] [Current]
Feedback Forum
2008-11-22 15:46:33 [6066575aa30c0611e452e930b1dff53d] [reply] 
Ook hier is de output produced by software verkeerd. De populatie variantie moet gelijk zijn aan 0.012. De nulhypothese moet gelijk zijn aan 0.152. De conclusie is ook verkeerd. Hier moet men ook de right one-sided confidence interval at 0.95 gebruiken omdat dit enkel de afwijking van het vetpercentage naar boven toe geeft en dit kan een economisch voordeel betekenen voor de producent. Verder kan men ook besluiten dat ookal gaan we uit van de nulhypothese gelijk aan 15,2% in plaats van 15% dan nog ligt het gemiddelde van de steekproef 15,46% lager dan 18,67% en dus binnen het 95% betrouwbaarheidsinterval.
2008-11-22 19:11:58 [c00776cbed2786c9c4960950021bd861] [reply] 
Er worden hier verkeerde getallen gebruikt in de berekening --> juiste tabel:

Population variance 0.012
Sample size 27
Null hypothesis (H0) 0.152
Confidence interval 0.95
Type of Interval Left tail Right tail
Two-sided confidence interval at 0.95 0.110680331179696 0.193319668820304
Left one-sided confidence interval at 0.95 0.117323440808296 +inf
Right one-sided confidence interval at 0.95 -inf 0.186676559191704

Weer maken we gebruik van de right one-sided betrouwbaarheidsinterval voor dezelfde reden als Q5.
Zowel de 0.152 als de 0.1546 liggen binnen dit betrouwbaarheidsinterval dus men kan besluiten dat de sample average consistent is met het vetproductiepercentage.
2008-11-24 16:04:37 [4679c4d03f1d346a85e79d87ba60ec2b] [reply] 
Goede methode met verkeerde gegevens. Population variance zou ook hier 0.012 moeten zijn, en de nulhypothese zou ook hier 0.152 moeten zijn. Correcte conclusie, bij een nulhypothese van 0.152 ligt het gemiddelde lager dan de right one-sided confidence interval van 0.186676... en ligt het dus binnen het betrouwbaarheidsinterval van 95 %. Ook hier zou gebruik gemaakt moeten worden van de one-sided confidence interval van de rechterkant. Ook hier is de rechterkant nauwkeuriger.

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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 time14 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 & 14 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24641&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]14 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=24641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24641&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 time14 seconds
R Server'George Udny Yule' @ 72.249.76.132






Testing Sample Mean with known Variance
Population variance1.2
Sample size27
Null hypothesis (H0)15.2
Confidence interval0.95
Type of IntervalLeft tailRight tail
Two-sided confidence interval at 0.9514.786803311797015.6131966882030
Left one-sided confidence interval at 0.9514.8532344080830+inf
Right one-sided confidence interval at 0.95-inf15.5467655919170
more information about confidence interval

\begin{tabular}{lllllllll}
\hline
Testing Sample Mean with known Variance \tabularnewline
Population variance & 1.2 \tabularnewline
Sample size & 27 \tabularnewline
Null hypothesis (H0) & 15.2 \tabularnewline
Confidence interval & 0.95 \tabularnewline
Type of Interval & Left tail & Right tail \tabularnewline
Two-sided confidence interval at  0.95 & 14.7868033117970 & 15.6131966882030 \tabularnewline
Left one-sided confidence interval at  0.95 & 14.8532344080830 & +inf \tabularnewline
Right one-sided confidence interval at  0.95 & -inf & 15.5467655919170 \tabularnewline
more information about confidence interval \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24641&T=1

[TABLE]
[ROW][C]Testing Sample Mean with known Variance[/C][/ROW]
[ROW][C]Population variance[/C][C]1.2[/C][/ROW]
[ROW][C]Sample size[/C][C]27[/C][/ROW]
[ROW][C]Null hypothesis (H0)[/C][C]15.2[/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]14.7868033117970[/C][C]15.6131966882030[/C][/ROW]
[ROW][C]Left one-sided confidence interval at  0.95[/C][C]14.8532344080830[/C][C]+inf[/C][/ROW]
[ROW][C]Right one-sided confidence interval at  0.95[/C][C]-inf[/C][C]15.5467655919170[/C][/ROW]
[ROW][C]more information about confidence interval[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24641&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 variance1.2
Sample size27
Null hypothesis (H0)15.2
Confidence interval0.95
Type of IntervalLeft tailRight tail
Two-sided confidence interval at 0.9514.786803311797015.6131966882030
Left one-sided confidence interval at 0.9514.8532344080830+inf
Right one-sided confidence interval at 0.95-inf15.5467655919170
more information about confidence interval


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1.2 ; par2 = 27 ; par3 = 15.2 ; par4 = 0.95 ;
Parameters (R input):
par1 = 1.2 ; par2 = 27 ; par3 = 15.2 ; 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')