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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_hypothesismean1.wasp
Title produced by softwareTesting Mean with known Variance - Critical Value
Date of computationThu, 13 Nov 2008 02:08:51 -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/t1226567404jzmkz09tooxnt3z.htm/, Retrieved Sun, 19 May 2024 09:25:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24498, Retrieved Sun, 19 May 2024 09:25:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Testing Mean with known Variance - Critical Value] [The pork quality ...] [2008-11-13 09:08:51] [0cebda6bbc99948f606f5db2560512ab] [Current]
-   P     [Testing Mean with known Variance - Critical Value] [correctie Q1 pork...] [2008-11-24 20:20:23] [74be16979710d4c4e7c6647856088456]
Feedback Forum
2008-11-24 09:22:05 [Anouk Greeve] [reply] 
De berekeningen zijn niet helemaal correct. In dit geval is de critical value (0,18468) groter dan de sample mean (0,1546= het steekproefgemiddelde). Hieruit kunnen we afleiden dat er sprake is van een toevallige afwijking tov het contractueel bepaalde vetgehalte (=15%).
We verwerpen de nulhypothese dus niet. Dat we de one-sided-test gebruiken klopt.
We dienen geen klacht in, omdat de contractueel afgesproken waardes niet overschreden worden.
2008-11-24 21:23:43 [Jasmine Hendrikx] [reply] 
Evaluatie Q1:
De juiste methode is gebruikt, maar er zijn verkeerde getallen ingevuld. Zo moet je bij population variance niet 1.2, maar 0.012 invullen. Hetzelfde geldt voor sample mean en voor de nulhypothese (je moet deze getallen nog delen door 100). Hieronder staat de URL met de juiste berekening: http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/24/t1227558158p1ogye6wa47tbb5.htm
Het gebruik van de one-tailed test is inderdaad een mogelijkheid. De student beargumenteert dit ook. Je zou hier nog bij kunnen zetten dat de leverancier alleen maar een economisch voordeel kan halen door te veel vet te leveren. Je zou ook van een two-tailed test kunnen uitgaan. Uit de vraag zouden we dit kunnen afleiden. Je zou zowel teveel vet als te weinig vet kunnen produceren. We zien dat de sample mean dan perfect ligt in het 95% betrouwbaarheidsinterval (two tailed). Er is dan geen sprake van een significant verschil. We gaan geen klacht indienen.
Doordat de student een verkeerde berekening heeft gebruikt, is de conclusie ook verkeerd. Wanneer we gebruik maken van de one-tailed test (we kijken naar de afwijking naar boven) dan zou je het volgende moeten vermelden: We zien dat de kritische waarde (18.47%) groter is dan het steekproefgemiddelde (15.46%). We kunnen hieruit afleiden dat er sprake is van een toevallige afwijking ten opzichte van het contractueel bepaalde vetgehalte (15%). De kritische waarde wordt dus niet overschreden, wat betekent dat we de nulhypothese niet verwerpen.
We dienen bijgevolg ook geen klacht in, omdat het verschil tussen de afgesproken 15% en het steekproefgemiddelde van 15.46% toe te schrijven is aan het toeval.

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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=24498&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=24498&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24498&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 Mean with known Variance
sample size27
population variance1.2
sample mean15.46
null hypothesis about mean15
type I error0.05
critical value (one-tailed)15.3467655919170
confidence interval (two-tailed)(sample mean)[ 15.0468033117970 , 15.8731966882030 ]
conclusion for one-tailed test
Reject the null hypothesis.
conclusion for two-tailed test
Reject the null hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
sample size & 27 \tabularnewline
population variance & 1.2 \tabularnewline
sample mean & 15.46 \tabularnewline
null hypothesis about mean & 15 \tabularnewline
type I error & 0.05 \tabularnewline
critical value (one-tailed) & 15.3467655919170 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 15.0468033117970 ,  15.8731966882030 ] \tabularnewline
conclusion for one-tailed test \tabularnewline
Reject the null hypothesis. \tabularnewline
conclusion for two-tailed test \tabularnewline
Reject the null hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24498&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]27[/C][/ROW]
[ROW][C]population variance[/C][C]1.2[/C][/ROW]
[ROW][C]sample mean[/C][C]15.46[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]15[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]15.3467655919170[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 15.0468033117970 ,  15.8731966882030 ][/C][/ROW]
[ROW][C]conclusion for one-tailed test[/C][/ROW]
[ROW][C]Reject the null hypothesis.[/C][/ROW]
[ROW][C]conclusion for two-tailed test[/C][/ROW]
[ROW][C]Reject the null hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24498&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24498&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 Mean with known Variance
sample size27
population variance1.2
sample mean15.46
null hypothesis about mean15
type I error0.05
critical value (one-tailed)15.3467655919170
confidence interval (two-tailed)(sample mean)[ 15.0468033117970 , 15.8731966882030 ]
conclusion for one-tailed test
Reject the null hypothesis.
conclusion for two-tailed test
Reject the null hypothesis


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 27 ; par2 = 1.2 ; par3 = 15.46 ; par4 = 15 ; par5 = 0.05 ;
Parameters (R input):
par1 = 27 ; par2 = 1.2 ; par3 = 15.46 ; par4 = 15 ; par5 = 0.05 ;
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)
par5<-as.numeric(par5)
c <- 'NA'
csn <- abs(qnorm(par5))
csn2 <- abs(qnorm(par5/2))
if (par3 == par4)
{
conclusion <- 'Error: the null hypothesis and sample mean must not be equal.'
conclusion2 <- conclusion
} else {
cleft <- par3 - csn2 * sqrt(par2) / sqrt(par1)
cright <- par3 + csn2 * sqrt(par2) / sqrt(par1)
c2 <- paste('[',cleft)
c2 <- paste(c2,', ')
c2 <- paste(c2,cright)
c2 <- paste(c2,']')
if ((par4 < cleft) | (par4 > cright))
{
conclusion2 <- 'Reject the null hypothesis'
} else {
conclusion2 <- 'Do not reject the null hypothesis'
}
}
if (par3 > par4)
{
c <- par4 + csn * sqrt(par2) / sqrt(par1)
if (par3 < c)
{
conclusion <- 'Do not reject the null hypothesis.'
} else {
conclusion <- 'Reject the null hypothesis.'
}
}
if (par3 < par4)
{
c <- par4 - csn * sqrt(par2) / sqrt(par1)
if (par3 > c)
{
conclusion <- 'Do not reject the null hypothesis.'
} else {
conclusion <- 'Reject the null hypothesis.'
}
}
c
conclusion
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm','Testing Mean with known Variance','learn more about Statistical Hypothesis Testing about the Mean when the Variance is known'),2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'sample size',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'population variance',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'sample mean',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'null hypothesis about mean',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'type I error',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ht_mean_knownvar.htm#overview','critical value (one-tailed)','about the critical value'),header=TRUE)
a<-table.element(a,c)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'confidence interval (two-tailed)
(sample mean)',header=TRUE)
a<-table.element(a,c2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'conclusion for one-tailed test',2,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,conclusion,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'conclusion for two-tailed test',2,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,conclusion2,2)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')