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R Software Module

rwasp_hypothesismean6.wasp

Title produced by software

Testing Sample Mean with known Variance - Confidence Interval

Date of computation

Tue, 11 Nov 2008 03:36:38 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/11/t12263998383g3ye17tal49k50.htm/, Retrieved Sun, 19 May 2024 09:01:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23290, Retrieved Sun, 19 May 2024 09:01:57 +0000

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Estimated Impact

164

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] [Pork quality test Q6] [2008-11-11 10:36:38] [821c4b3d195be8e737cf8c9dc649d3cf] [Current]
F   P     [Testing Sample Mean with known Variance - Confidence Interval] [Q6] [2008-11-12 14:31:32] [a0c3f7f6bb6d3d65b8bcf25e6a3c7584] 
F         [Testing Sample Mean with known Variance - Confidence Interval] [] [2008-11-12 14:32:54] [f8005fb082f70566c42409d36c038970] 

Feedback Forum

2008-11-20 13:27:39 [Gert-Jan Geudens] [reply] 
Ook hier is het antwoord -net zoals in Q5- niet helemaal correct. De student gebruikt de Left one-sided confidence interval at 0.95 en Right one-sided confidence interval at 0.95 om het interval op te stellen. Uiteraard is dit niet correct en moeten we enkel de Right one-sided confidence interval at 0.95 gebruiken aangezien we een vermoeden hebben van teveel vet. Het nieuwe betrouwbaarheidsinterval is dan gelijk aan '-oneindig ; 18.67%'. Het steekproefgemiddelde ligt mooi binnen dit interval en dus is het wel degelijk consistent met het vet-productie percentage.
2008-11-23 15:10:42 [Maarten Van Gucht] [reply] 
Ook hier is het antwoord -net zoals in Q5- niet helemaal correct. Ook hier gebruiken we de rechterstaart omdat de rechterstaart is nauwkeuriger, de volledige 5% wordt toegewezen aan de rechterkant.  
(bij de two-sided wordt de foutmarge over de twee tails verdeeld, wat maakt dat de resultaten nog extremer worden voor de two-sided.) 
Ook al gaan we uit van een nulhypothese van 15.2% in plaats van 15%, dan nog ligt het gemiddelde van de steekproef 0.1546 lager dan 0.1893 en dus binnen het 95%-betrouwbaarheidsinterval.
2008-11-23 18:56:51 [Aurélie Van Impe] [reply] 
Hier moet ongeveer hetzelfde antwoord komen als bij vraag 5. Bijgevolg is het antwoord van de student opnieuw niet helemaal correct. Je moet enkel gebruik maken van de rechtse staart, omdat we uitgaan van teveel vet. Ook al gaan we uit van een nulhypothese van 15.2% in plaats van 15%, dan nog ligt het gemiddelde van de steekproef 0.1546 lager dan 0.1893 en dus binnen het 95%-betrouwbaarheidsinterval.
2008-11-24 10:35:27 [Lennart Holemans] [reply] 
Het antwoord is net zoals in Q5 niet correct. .De student moet enkel de Right one-sided confidence interval at 0.95 gebruiken aangezien we een vermoeden hebben van teveel vet. Het nieuwe betrouwbaarheidsinterval is dan gelijk aan '-oneindig ; 18.67%'. Het steekproefgemiddelde ligt binnen dit interval en dus is het wel degelijk consistent met het vet-productie percentage.

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=23290&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=23290&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23290&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Testing Sample Mean with known Variance
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
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=23290&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=23290&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23290&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Testing Sample Mean with known Variance
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
more information about confidence interval

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')

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