# ::Free Statistics and Forecasting Software::

v1.2.1

### :: Testing Mean with known Variance - Critical Value - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the critical values for one- and two-sided hypothesis tests about the mean. In this test it is assumed that the population variance is known.

 Send output to: Browser Blue - Charts White Browser Black/White CSV Sample size Population Variance Sample Mean Null Hypothesis about mean Type I error (alpha)

 Source code of R 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." } } print(c) print(conclusion) load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Testing Mean with known Variance",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,"critical value (one-tailed)",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")
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 Cite this software as: Wessa P., (2016), Testing Mean with known Variance (v1.0.7) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_hypothesismean1.wasp/ The R code is based on : Xycoon, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/ht_mean_knownvar.htm#ex1
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 To cite Wessa.net in publications use:Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education, version 1.2.1, URL https://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.2.1Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net