With regards to **t-test**, the function `t.test()`

in R may be used. This is a rather simple function which performs both one- and two-sample t-tests (it is thus likely that we will meet that function elsewhere in this website).

Assuming that you have stored your sample data in the variable called `scores`

, the command to use is `t.test(scores, alternative="ALT", mu = Y)`

where:

`ALT`

shall be replaced by either`greater`

or`less`

or`two.sided`

depending of 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`

).

- the sample mean is
`Y`

shall be replaced by the value of the population mean.

Using our previous example, this looks like:

`t.test(scores, alternative="greater", mu=120)`

```
##
## One Sample t-test
##
## data: scores
## t = 3.9591, df = 39, p-value = 0.0001547
## alternative hypothesis: true mean is greater than 120
## 95 percent confidence interval:
## 123.6476 Inf
## sample estimates:
## mean of x
## 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 `t.test()`

. This alternative hypothesis `Ha`

is considered valid when the p-value is less than 0.05.

Read more about `t.test()`

and find more options by clicking here or there or by simply typing `?t.test`

in the R console.