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.

- the sample mean is

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.