4. Run a one-sample z-test.


With regards to z-test, there is NO z.test() function in R, unfortunately. However, the package TeachingDemos contains a z.test() function which will be helpful. You must install and load the TeachingDemos package in the same manner as you previously installed pastecs (see here).

Assuming that you have stored your sample data in the variable data, the command to use is z.test(data, mu = Y, stdev = W, alternative="XXX") where:

  • Y shall be replaced by the value of the population mean,
  • W shall be replaced by the standard deviation of the population (since it is known),
  • “XXX” shall be replaced by “greater” OR “less” OR “two.sided” depending of your alternative hypothesis Ha. The null hypothesis Hstates that the sample mean is NOT different from the population mean. Your alternative hypothesis Ha is one of the following:
    • the sample mean is greater than the population mean >> use “greater”
    • the sample mean is less than the population mean >> use “less”
    • the sample mean is either smaller or greater than the population mean >> use “two.sided”.
More info about TeachingDemos is available here.
R returns several lines of text. One of them provides a p-value while the next line states the alternative hypothesis which depends on the parameter alternative=”XXX” that you have entered in the z.test(). This alternative hypothesis Ha is considered valid when the p-value is less than 0.05.