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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 07:13:27 -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/t12265856240b4s2rln63zwxsc.htm/, Retrieved Sun, 19 May 2024 09:21:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24618, Retrieved Sun, 19 May 2024 09:21:04 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

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] [] [2008-11-13 14:13:27] [ffe1355fa7fe5626118ee2c4cacbba88] [Current]
Feedback Forum
2008-11-14 16:10:30 [407693b66d7f2e0b350979005057872d] [reply] 
Dit antwoord is niet correct.

We gebruiken de 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.
We gebruiken hier de rechter staart omdat deze nauwkeuriger is omdat de volledige foutmarge van 5% zich in deze staart bevindt. (bij de two-sided confidence interval wordt de 5% verdeeld over zowel de linkse als de rechtse staart, wat de resultaten van de two-sided extremer maakt)
De sample-mean ligt onder0.189276559191704 dus binnen het betrouwbaarheidinterval van 95%.
2008-11-15 10:35:04 [a7d9990a66ef13b6ce566dbfd4dc5418] [reply] 
Ook hier zit de student er volledig naast.
We gebruiken de one-sided conficence interval van de right-tail, omdat enkel de afwijking van het vetpercentage naar boven toe een economisch voordeel voor de producent kan betekenen.
Doordat de volledige 5%(foutmarge) toegewezen wordt aan de rechtkant, is de rechter staart nauwkeuriger.
De sample mean, 0.1546, ligt onder 0.189276559191704 en dus binnen het 95%-betrouwbaarheidsinterval.
2008-11-24 14:50:02 [Sofie Sergoynne] [reply] 
Er is geen interpretatie bij de output gegeven. De output is ook fout. Men gebruikt in de output 15% en 15.46% ipv 0.15% en 0.1546%. Dit zorgt al voor een foute output. Indien men dit wel zou doen... kan men de olgende conclusies trekken. We gebruiken de 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.
De rechter staart is nauwkeuriger, omdat de volledige 5% (foutmarge) toegewezen wordt aan de rechterkant.
(bij de two-sided confidence interval wordt de 5% verdeeld over zowel de linkse als de rechtse staart, wat de resultaten van de two-sided extremer maakt)
De sample mean (0.1546) ligt onder 0.189276559191704 en dus binnen het 95%-betrouwbaarheidsinterval.


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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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24618&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24618&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'Gwilym Jenkins' @ 72.249.127.135






Testing Mean with known Variance
sample size27
population variance1.2
sample mean15.45
null hypothesis about mean15
type I error0.05
critical value (one-tailed)15.3467655919170
confidence interval (two-tailed)(sample mean)[ 15.0368033117970 , 15.8631966882030 ]
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 & 15.45 \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) & [ 15.0368033117970 ,  15.8631966882030 ] \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=24618&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]15.45[/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][ 15.0368033117970 ,  15.8631966882030 ][/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=24618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24618&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 mean15.45
null hypothesis about mean15
type I error0.05
critical value (one-tailed)15.3467655919170
confidence interval (two-tailed)(sample mean)[ 15.0368033117970 , 15.8631966882030 ]
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 = 15,45 ; par4 = 15 ; par5 = 0.05 ;
Parameters (R input):
par1 = 27 ; par2 = 1.2 ; par3 = 15.45 ; 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')