## Free Statistics

of Irreproducible Research!

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 computationFri, 22 Oct 2010 12:25:10 +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/22/t1287750250rtftpfew1vuch3k.htm/, Retrieved Sun, 03 Dec 2023 04:31:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87422, Retrieved Sun, 03 Dec 2023 04:31:51 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
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] [IM 1 - Female - 2...] [2010-10-22 12:25:10] [18ef3d986e8801a4b28404e69e5bf56b] [Current]
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 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 0 seconds R Server 'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87422&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87422&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87422&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 0 seconds R Server 'George Udny Yule' @ 72.249.76.132

 Testing Mean with known Variance sample size 63 population variance 14 sample mean 21 null hypothesis about mean 20 type I error 0.05 critical value (one-tailed) 20.7753914357844 confidence interval (two-tailed)(sample mean) [ 20.0760641171002 , 21.9239358828998 ] 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 & 63 \tabularnewline
population variance & 14 \tabularnewline
sample mean & 21 \tabularnewline
null hypothesis about mean & 20 \tabularnewline
type I error & 0.05 \tabularnewline
critical value (one-tailed) & 20.7753914357844 \tabularnewline
confidence interval (two-tailed)(sample mean) & [ 20.0760641171002 ,  21.9239358828998 ] \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=87422&T=1

[TABLE]
[ROW][C]Testing Mean with known Variance[/C][/ROW]
[ROW][C]sample size[/C][C]63[/C][/ROW]
[ROW][C]population variance[/C][C]14[/C][/ROW]
[ROW][C]sample mean[/C][C]21[/C][/ROW]
[ROW][C]null hypothesis about mean[/C][C]20[/C][/ROW]
[ROW][C]type I error[/C][C]0.05[/C][/ROW]
[ROW][C]critical value (one-tailed)[/C][C]20.7753914357844[/C][/ROW]
[ROW][C]confidence interval (two-tailed)(sample mean)[/C][C][ 20.0760641171002 ,  21.9239358828998 ][/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=87422&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87422&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Testing Mean with known Variance sample size 63 population variance 14 sample mean 21 null hypothesis about mean 20 type I error 0.05 critical value (one-tailed) 20.7753914357844 confidence interval (two-tailed)(sample mean) [ 20.0760641171002 , 21.9239358828998 ] conclusion for one-tailed test Reject the null hypothesis. conclusion for two-tailed test Reject the null hypothesis

Parameters (Session):
par1 = 63 ; par2 = 14 ; par3 = 21 ; par4 = 20 ; par5 = 0.05 ;
Parameters (R input):
par1 = 63 ; par2 = 14 ; par3 = 21 ; par4 = 20 ; 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.'}}cconclusionload(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')