With regards to z-test, there is NO z.test() function in the original R package, unfortunately. However, the package TeachingDemos contains a z.test() function which will be helpful. We therefore start with installing and loading TeachingDemos:

install.packages("TeachingDemos")
library(TeachingDemos)

Assuming that you have stored your sample data in the variable scores, the command to use is z.test(scores, mu = Y, stdev = W, alternative="ALT") 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 one of the conditions to run the test, see here),
• ALT shall be replaced by either greater or less or two.sided depending on your alternative hypothesis Ha. The null hypothesis H0 states 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 (in that case, use greater),
  • the sample mean is less than the population mean >> (in that case, use less)
  • the sample mean is either smaller or greater than the population mean (in that case, use two.sided). More info about TeachingDemos is available here.

Considering our previous example, this would look like:

z.test(scores, alternative="greater", mu=120, stdev=UNKNOWN)

However, as stated in the code, the standard deviation is unknown. Therefore, a z.test cannot be used.

IF the standand deviation was previously know and equal to 15, this would have been the code and the corresponding output:

z.test(scores, alternative="greater", mu=120, stdev=15)

## 
##  One Sample z-test
## 
## data:  scores
## z = 2.6774, n = 40.0000, Std. Dev. = 15.0000, Std. Dev. of the
## sample mean = 2.3717, p-value = 0.00371
## alternative hypothesis: true mean is greater than 120
## 95 percent confidence interval:
##  122.4489      Inf
## sample estimates:
## mean of scores 
##         126.35

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 that you have entered in the z.test(). This alternative hypothesis Ha is considered valid when the p-value is less than 0.05.

Read more about z.test() by simply typing ?z.test in the R console.

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