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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, 18 Oct 2010 11:56:04 +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/18/t12874030407ip7033kl379dr6.htm/, Retrieved Sun, 28 Apr 2024 10:33:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=84710, Retrieved Sun, 28 Apr 2024 10:33:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact402

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Testing Mean with known Variance - Critical Value] [] [2010-10-18 11:56:04] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
- RMP     [Testing Variance - Confidence Intervals for Sample Variance] [Ws4 - Q8] [2010-10-24 18:55:58] [b11c112f8986de933f8b95cd30e75cc2]
F RMP     [Testing Variance - Critical Value (Region)] [WS4 - Q8 M] [2010-10-24 18:58:28] [b11c112f8986de933f8b95cd30e75cc2]
F           [Testing Variance - Critical Value (Region)] [WS4 - Q8 F] [2010-10-24 18:59:38] [b11c112f8986de933f8b95cd30e75cc2]
F RM        [Testing Mean with known Variance - Sample Size] [WS4 - Q9] [2010-10-24 19:18:48] [b11c112f8986de933f8b95cd30e75cc2]
F RM        [Testing Mean with known Variance - Sample Size] [WS4 - Q10] [2010-10-24 19:21:33] [b11c112f8986de933f8b95cd30e75cc2]
F RM        [Minimum Sample Size - Testing Mean] [WS4 - Q11] [2010-10-24 19:28:16] [b11c112f8986de933f8b95cd30e75cc2]
-   P       [Testing Variance - Critical Value (Region)] [Question 8 Men] [2010-10-26 20:31:09] [ff7c1e95cf99a1dae07ec89975494dde]
- RMP     [Testing Variance - Confidence Intervals for Sample Variance] [] [2010-10-26 11:51:58] [d87a19cd5db53e12ea62bda70b3bb267]
- RMP     [Testing Mean with known Variance - Type II Error] [] [2010-10-26 12:03:10] [d87a19cd5db53e12ea62bda70b3bb267]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [] [2010-10-26 12:07:45] [d87a19cd5db53e12ea62bda70b3bb267]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [] [2010-11-11 16:09:15] [74be16979710d4c4e7c6647856088456]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [post1-pre / treat...] [2010-11-11 16:17:20] [74be16979710d4c4e7c6647856088456]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [post1-pre / treat...] [2010-11-11 16:19:54] [74be16979710d4c4e7c6647856088456]
F RMPD    [Testing Mean with unknown Variance - Critical Value] [post1-pre / treat...] [2010-11-11 16:23:45] [74be16979710d4c4e7c6647856088456]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [post1-pre / treat...] [2010-11-11 16:23:45] [74be16979710d4c4e7c6647856088456]
- RMP     [Testing Mean with known Variance - Sample Size] [Question 9 Academ...] [2010-11-11 19:40:44] [64a7ae6044525e7ca71ecb546c042c9e]
- RMP     [Testing Mean with known Variance - Sample Size] [Question 10 Acade...] [2010-11-11 20:02:21] [74be16979710d4c4e7c6647856088456]
- RMP     [Testing Mean with known Variance - Sample Size] [Question 10 Acade...] [2010-11-11 20:02:21] [64a7ae6044525e7ca71ecb546c042c9e]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [Question 5 Academ...] [2010-11-11 20:20:34] [64a7ae6044525e7ca71ecb546c042c9e]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [Question 4 Academ...] [2010-11-11 20:42:24] [64a7ae6044525e7ca71ecb546c042c9e]
- RMPD    [One Sample Tests about the Mean] [Question 6 Academ...] [2010-11-11 20:58:54] [64a7ae6044525e7ca71ecb546c042c9e]
- RMP     [Testing Mean with known Variance - Sample Size] [Question 9 Academ...] [2010-11-11 21:19:23] [64a7ae6044525e7ca71ecb546c042c9e]
- RMP     [Testing Mean with known Variance - Sample Size] [Question 10 Acade...] [2010-11-11 21:30:09] [6414ffdb872b907ae8a6798e4f5e9947]
- RMP     [Minimum Sample Size - Testing Mean] [Question 11 Acade...] [2010-11-11 21:45:16] [64a7ae6044525e7ca71ecb546c042c9e]
- R P     [Testing Mean with known Variance - Critical Value] [vraag x] [2010-11-18 13:16:45] [f15cf5036ae52d4243ad71d4fb151dbe]
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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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84710&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=84710&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84710&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Testing Mean with known Variance
sample size60
population variance40000
sample mean2460
null hypothesis about mean2400
type I error0.05
critical value (one-tailed)2442.46993802755
confidence interval (two-tailed)(sample mean)[ 2409.39394752473 , 2510.60605247527 ]
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 & 60 \tabularnewline
population variance & 40000 \tabularnewline
sample mean & 2460 \tabularnewline
null hypothesis about mean & 2400 \tabularnewline
type I error & 0.05 \tabularnewline
critical value (one-tailed) & 2442.46993802755 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 2409.39394752473 ,  2510.60605247527 ] \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=84710&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]60[/C][/ROW]
[ROW][C]population variance[/C][C]40000[/C][/ROW]
[ROW][C]sample mean[/C][C]2460[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]2400[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]2442.46993802755[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 2409.39394752473 ,  2510.60605247527 ][/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=84710&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84710&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 size60
population variance40000
sample mean2460
null hypothesis about mean2400
type I error0.05
critical value (one-tailed)2442.46993802755
confidence interval (two-tailed)(sample mean)[ 2409.39394752473 , 2510.60605247527 ]
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 = 60 ; par2 = 40000 ; par3 = 2460 ; par4 = 2400 ; par5 = 0.05 ;
Parameters (R input):
par1 = 60 ; par2 = 40000 ; par3 = 2460 ; par4 = 2400 ; 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')