# ::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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