The one-sample Z-test in R

We can run such a test in R, using the package BSDA, and its function z.test. Lets try it.

# install.packages("BSDA")   #first install the library, if you have not this library installed....simply remove the # sign and run this line
library ("BSDA")           #load the library
Sample=c(9.7, 9.7, 8.9, 9.2, 9.4, 9.1, 9.5, 9.6, 8.9, 9.1, 9.5, 9.2, 9.5, 9.4, 9.6, 9.2, 9.9, 10, 9.3, 9.6) #lets put the values in a vector
PopulationMean= 9.5 #this is the population mean...or the historical time it has taken people to run 100m
PopulationSD=0.2 #this is the population standard deviation

z.test(x=Sample, alternative = "less", mu = PopulationMean, sigma.x = PopulationSD, conf.level = 0.95)

#the parameters needed to run a Z-test are self-explanatory. x is the array with your sample data. alternative is the type of test to run, in this case we want to check is the sample is less than the population mean. mu is the population mean, and sigma.x is the standard deviation of the population. This function ask for the confidence level, which as we indicated before is the complement to the level of significance we use, in our case our significance level is 0.05, so the confidence level will be 0.95

The results will look like the image below, which are nearly identical to our hand calculation. a

R-results for a one-sample z-test

Figure 10.5: R-results for a one-sample z-test