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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwareTesting Mean with known Variance - Critical Value
Date of computationTue, 08 Nov 2011 12:37:08 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/08/t1320773847htu3iz5frxpa2aj.htm/, Retrieved Tue, 16 Apr 2024 15:07:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=140808, Retrieved Tue, 16 Apr 2024 15:07:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Factor Analysis] [Sleep in Mammals ...] [2010-03-21 11:39:53] [b98453cac15ba1066b407e146608df68]
- RMPD  [Testing Mean with unknown Variance - Critical Value] [Hypothesis Test a...] [2010-10-19 11:45:26] [b98453cac15ba1066b407e146608df68]
-   PD    [Testing Mean with unknown Variance - Critical Value] [WS4 - Question 5] [2010-10-25 19:47:30] [1f5baf2b24e732d76900bb8178fc04e7]
- RMPD      [Testing Mean with known Variance - Critical Value] [WS4 - Question 8 ...] [2010-10-25 20:17:41] [1f5baf2b24e732d76900bb8178fc04e7]
F R P         [Testing Mean with known Variance - Critical Value] [WS4 Q8] [2010-10-26 18:21:42] [afe9379cca749d06b3d6872e02cc47ed]
- R P           [Testing Mean with known Variance - Critical Value] [taak 8 mannen] [2011-10-25 11:36:52] [380049693c521f4999989215fb37aeca]
-   P             [Testing Mean with known Variance - Critical Value] [] [2011-10-25 22:51:15] [493236dcc414c5f9e1823f06b33a5ad6]
-  MP                 [Testing Mean with known Variance - Critical Value] [] [2011-11-08 17:37:08] [76a85a4cc6ea7903d92a0f5b9d2872d3] [Current]
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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 time0 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 0 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140808&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140808&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140808&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 time0 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Testing Mean with known Variance
sample size98
population variance13
sample mean20.2857142857143
null hypothesis about mean20
type I error0.35
critical value (one-tailed)20.1403397555142
confidence interval (two-tailed)(sample mean)[ 19.945322211973 , 20.6261063594556 ]
conclusion for one-tailed test
Reject the null hypothesis.
conclusion for two-tailed test
Do not reject the null hypothesis

\begin{tabular}{lllllllll}
\hline
Testing Mean with known Variance \tabularnewline
sample size & 98 \tabularnewline
population variance & 13 \tabularnewline
sample mean & 20.2857142857143 \tabularnewline
null hypothesis about mean & 20 \tabularnewline
type I error & 0.35 \tabularnewline
critical value (one-tailed) & 20.1403397555142 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 19.945322211973 ,  20.6261063594556 ] \tabularnewline
conclusion for one-tailed test \tabularnewline
Reject the null hypothesis. \tabularnewline
conclusion for two-tailed test \tabularnewline
Do not reject the null hypothesis \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=140808&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]98[/C][/ROW]
[ROW][C]population variance[/C][C]13[/C][/ROW]
[ROW][C]sample mean[/C][C]20.2857142857143[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]20[/C][/ROW]
[ROW][C]type I error[/C][C]0.35[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]20.1403397555142[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 19.945322211973 ,  20.6261063594556 ][/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]Do not reject the null hypothesis[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=140808&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=140808&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 size98
population variance13
sample mean20.2857142857143
null hypothesis about mean20
type I error0.35
critical value (one-tailed)20.1403397555142
confidence interval (two-tailed)(sample mean)[ 19.945322211973 , 20.6261063594556 ]
conclusion for one-tailed test
Reject the null hypothesis.
conclusion for two-tailed test
Do not reject the null hypothesis


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 98 ; par2 = 13 ; par3 = 20.2857142857143 ; par4 = 20 ; par5 = 0.35 ;
Parameters (R input):
par1 = 98 ; par2 = 13 ; par3 = 20.2857142857143 ; par4 = 20 ; par5 = 0.35 ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')