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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 12:07:18 +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/t1287403620c6k2n1bkyppum68.htm/, Retrieved Fri, 09 May 2025 10:52:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=84727, Retrieved Fri, 09 May 2025 10:52:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact477

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 12:07:18] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
F RMPD    [Population Mean Test] [WS4 Q1.1] [2010-10-22 12:43:07] [afe9379cca749d06b3d6872e02cc47ed]
F    D      [Population Mean Test] [WS4 Q2.2] [2010-10-24 10:34:25] [afe9379cca749d06b3d6872e02cc47ed]
-    D        [Population Mean Test] [WS4 Q2.3] [2010-10-24 10:43:20] [afe9379cca749d06b3d6872e02cc47ed]
F    D        [Population Mean Test] [WS4 Q2.3] [2010-10-24 10:43:20] [afe9379cca749d06b3d6872e02cc47ed]
-               [Population Mean Test] [voorbeeld 3] [2011-10-24 13:02:09] [74be16979710d4c4e7c6647856088456]
-                 [Population Mean Test] [WS4 Blog3] [2011-10-25 17:49:23] [f3a3c3f0a4b96c7d24d9b159bb15fbc3]
-                 [Population Mean Test] [] [2011-10-25 20:44:25] [74be16979710d4c4e7c6647856088456]
- RMPD          [Testing Mean with unknown Variance - Critical Value] [WS 4 Q 2 DD] [2011-10-25 14:12:42] [4f1f864fb932bb9c9d0c6cb0c11f4a44]
-               [Population Mean Test] [WS 4 - Question 2.3] [2012-10-23 16:45:51] [74be16979710d4c4e7c6647856088456]
-             [Population Mean Test] [voorbeeld 2] [2011-10-24 13:00:04] [74be16979710d4c4e7c6647856088456]
-               [Population Mean Test] [WS4 Blog2] [2011-10-25 17:48:35] [f3a3c3f0a4b96c7d24d9b159bb15fbc3]
-               [Population Mean Test] [] [2011-10-25 20:41:40] [74be16979710d4c4e7c6647856088456]
- RMPD        [Testing Mean with known Variance - Critical Value] [ws4 Q2.2] [2011-10-25 11:15:49] [2c786c21adba4dd4c8af44dce5258f06]
-             [Population Mean Test] [WS 4 - Question 2.1] [2012-10-23 16:43:36] [74be16979710d4c4e7c6647856088456]
-    D      [Population Mean Test] [WS IV question 2 ...] [2011-10-21 14:26:27] [74be16979710d4c4e7c6647856088456]
-           [Population Mean Test] [voorbeeld 1] [2011-10-24 12:53:42] [74be16979710d4c4e7c6647856088456]
-             [Population Mean Test] [WS 4 Blog1] [2011-10-25 17:45:31] [74be16979710d4c4e7c6647856088456]
-             [Population Mean Test] [WS4 blog 1] [2011-10-25 17:47:31] [f3a3c3f0a4b96c7d24d9b159bb15fbc3]
-             [Population Mean Test] [] [2011-10-25 20:39:21] [74be16979710d4c4e7c6647856088456]
-           [Population Mean Test] [WS 4 - Question 1.1] [2012-10-23 16:39:11] [74be16979710d4c4e7c6647856088456]
- R P     [Testing Mean with known Variance - Critical Value] [] [2010-10-22 14:58:59] [56d90b683fcd93137645f9226b43c62b]
- RMP     [Minimum Sample Size - Testing Mean] [Question 11] [2010-10-23 22:05:14] [b1e5ec7263cdefe98ec76e1a1363de05]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [] [2010-10-23 22:06:48] [b1e5ec7263cdefe98ec76e1a1363de05]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [q11] [2010-10-23 22:06:48] [b1e5ec7263cdefe98ec76e1a1363de05]
- RMP     [Minimum Sample Size - Testing Mean] [question 11] [2010-10-23 22:29:53] [b1e5ec7263cdefe98ec76e1a1363de05]
- RMP     [Testing Variance - p-value (probability)] [WS4 Question 8] [2010-10-26 17:07:31] [abf4ff90b26c6b37be4a30063b404639]
- RMP       [Testing Mean with known Variance - Sample Size] [WS4 Question 9] [2010-10-26 17:20:01] [abf4ff90b26c6b37be4a30063b404639]
-             [Testing Mean with known Variance - Sample Size] [WS4 Question 10] [2010-10-26 17:22:44] [abf4ff90b26c6b37be4a30063b404639]
- RM          [Minimum Sample Size - Testing Mean] [WS4 Question 11] [2010-10-26 17:29:09] [abf4ff90b26c6b37be4a30063b404639]
F RMP     [Testing Variance - p-value (probability)] [] [2010-10-26 17:07:32] [1ad9dd03b6c5806e9fe90049663fcef1]
- RMP     [Testing Variance - p-value (probability)] [WS4 Question 8 fe...] [2010-10-26 17:09:23] [abf4ff90b26c6b37be4a30063b404639]
F RMP     [Testing Variance - p-value (probability)] [] [2010-10-26 17:09:34] [1ad9dd03b6c5806e9fe90049663fcef1]
-   P     [Testing Mean with known Variance - Critical Value] [workshop 1 Q2] [2010-11-11 13:28:04] [9f313cc7203314d73bf17d2b325aee79]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [Workshop 1 Q2] [2010-11-11 16:17:03] [9f313cc7203314d73bf17d2b325aee79]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [Workshop 1 Q2] [2010-11-11 16:23:48] [9f313cc7203314d73bf17d2b325aee79]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [workshop 1 Q3] [2010-11-11 16:38:29] [9f313cc7203314d73bf17d2b325aee79]
- RM      [Testing Variance - Confidence Intervals for Sample Variance] [workshop 1 Q8] [2010-11-11 17:59:26] [9f313cc7203314d73bf17d2b325aee79]
- RM D    [Testing Mean with unknown Variance - Critical Value] [workshop 1 Q4] [2010-11-11 18:13:42] [9f313cc7203314d73bf17d2b325aee79]
- RM D    [Testing Mean with unknown Variance - Critical Value] [workshop 1 Q5] [2010-11-11 18:21:16] [9f313cc7203314d73bf17d2b325aee79]
- RMP     [] [] [-0001-11-30 00:00:00] [a7c91bc614e4e21e8b9c8593f39a36f1]
- RMPD    [Testing Mean with unknown Variance - Critical Value] [Workshop1Part1Q1H...] [2010-11-12 01:42:19] [a7c91bc614e4e21e8b9c8593f39a36f1]
F    D      [Testing Mean with unknown Variance - Critical Value] [Workshop1Part1Q2H...] [2010-11-12 01:57:53] [a7c91bc614e4e21e8b9c8593f39a36f1]
-    D        [Testing Mean with unknown Variance - Critical Value] [Workshop1Part1Q2H...] [2010-11-12 02:06:33] [a7c91bc614e4e21e8b9c8593f39a36f1]
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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=84727&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=84727&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84727&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 size100
population variance0.25
sample mean11.85
null hypothesis about mean12
type I error0.01
critical value (one-tailed)11.8836826062980
confidence interval (two-tailed)(sample mean)[ 11.7212085348226 , 11.9787914651774 ]
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 & 100 \tabularnewline
population variance & 0.25 \tabularnewline
sample mean & 11.85 \tabularnewline
null hypothesis about mean & 12 \tabularnewline
type I error & 0.01 \tabularnewline
critical value (one-tailed) & 11.8836826062980 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 11.7212085348226 ,  11.9787914651774 ] \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=84727&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]100[/C][/ROW]
[ROW][C]population variance[/C][C]0.25[/C][/ROW]
[ROW][C]sample mean[/C][C]11.85[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]12[/C][/ROW]
[ROW][C]type I error[/C][C]0.01[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]11.8836826062980[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 11.7212085348226 ,  11.9787914651774 ][/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=84727&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84727&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 size100
population variance0.25
sample mean11.85
null hypothesis about mean12
type I error0.01
critical value (one-tailed)11.8836826062980
confidence interval (two-tailed)(sample mean)[ 11.7212085348226 , 11.9787914651774 ]
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 = 100 ; par2 = 0.25 ; par3 = 11.85 ; par4 = 12 ; par5 = 0.01 ;
Parameters (R input):
par1 = 100 ; par2 = 0.25 ; par3 = 11.85 ; par4 = 12 ; par5 = 0.01 ;
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')