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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_hypothesismean1.wasp
Title produced by softwareTesting Mean with known Variance - Critical Value
Date of computationMon, 25 Oct 2010 20:11:53 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/25/t1288037807j251ub9vrqoh6bo.htm/, Retrieved Mon, 29 Apr 2024 22:06:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=88482, Retrieved Mon, 29 Apr 2024 22:06:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

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 - task 4] [2010-10-25 19:40:58] [8ef49741e164ec6343c90c7935194465]
-    D      [Testing Mean with unknown Variance - Critical Value] [WS4 - task 5] [2010-10-25 19:48:43] [8ef49741e164ec6343c90c7935194465]
-             [Testing Mean with unknown Variance - Critical Value] [WS4 - task 6] [2010-10-25 19:58:39] [8ef49741e164ec6343c90c7935194465]
F               [Testing Mean with unknown Variance - Critical Value] [WS4 - task 6] [2010-10-25 19:59:58] [8ef49741e164ec6343c90c7935194465]
F RM D              [Testing Mean with known Variance - Critical Value] [WS4 - task 8 (male)] [2010-10-25 20:11:53] [934c3727858e074bf543f25f5906ed72] [Current]
-                     [Testing Mean with known Variance - Critical Value] [WS4 - task 8 (fem...] [2010-10-25 20:19:59] [8ef49741e164ec6343c90c7935194465]
-   P                   [Testing Mean with known Variance - Critical Value] [WS 4 task 8 (vrou...] [2010-10-26 18:36:31] [8214fe6d084e5ad7598b249a26cc9f06]
- RM                  [Testing Mean with known Variance - Sample Size] [WS4 - task 9] [2010-10-25 20:27:24] [74be16979710d4c4e7c6647856088456]
- RM                  [Testing Mean with known Variance - Sample Size] [WS4 - task 9] [2010-10-25 20:27:24] [8ef49741e164ec6343c90c7935194465]
-                       [Testing Mean with known Variance - Sample Size] [WS4 - task 9] [2010-10-25 20:30:49] [8ef49741e164ec6343c90c7935194465]
-   P                     [Testing Mean with known Variance - Sample Size] [WS 4 task 10 - Ch...] [2010-10-26 19:30:59] [8214fe6d084e5ad7598b249a26cc9f06]
F RM                    [Minimum Sample Size - Testing Mean] [WS4 - task 11] [2010-10-25 20:36:53] [8ef49741e164ec6343c90c7935194465]
-   P                   [Testing Mean with known Variance - Sample Size] [WS 4 task 9 - Cha...] [2010-10-26 19:26:53] [8214fe6d084e5ad7598b249a26cc9f06]
F   P                 [Testing Mean with known Variance - Critical Value] [WS 4 task 8 (mann...] [2010-10-26 18:34:08] [8214fe6d084e5ad7598b249a26cc9f06]
Feedback Forum
2010-11-02 13:47:35 [Michael Van Goethem] [reply] 
Je moet de one sample test about the mean gebruiken. Via de one sample t-test krijgen we de p-waarde. Je gebruikt de gegevens van de kolom I1M uit excel. Het gaat hier om een two-sided test. En CI = 0.95. Als je dit laat berekenen door de blog kom je een p-value uit van 0.435. Hoe kleiner de p-waarde, hoe significanter het verschil of de afwijking van de nulhypothese.
2010-11-02 13:48:41 [Michael Van Goethem] [reply] 
Sorry, de feedback hierboven is verkeerd. Dit is de juiste:

We dienen eerst de standaardafwijking en het gemiddelde te berekenen in het excelbestand. De berekening voor de mannen is triviaal (deze komt exact overeen met de variantie uit de steekproef = 13). De berekening voor de vrouwen is anders, we krijgen een variantie die verschillend is van 13. Dit wil niet zeggen dat de variantie voor vrouwen groter is dan 13, maar wel dat het significant verschillend is.

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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 time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=88482&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]4 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=88482&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=88482&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






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)[ 19.9453222119730 , 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) & [ 19.9453222119730 ,  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=88482&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][ 19.9453222119730 ,  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=88482&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=88482&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)[ 19.9453222119730 , 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 = 0.95 ; par2 = 20 ;
Parameters (R input):
par1 = 98 ; par2 = 13 ; par3 = 20.2857142857143 ; par4 = 20 ; par5 = 0.35 ;
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')