## One Sample T Tests

The R function `t.test` (on-line help) does t tests and confidence intervals.

The example done on the confidence intervals page also does a test, although the default test is not necessarily the one you want.

Other arguments to the `t.test` function are `mu`, which specifies hypothesized value under H0 other than zero, and `alternative`, which allows for upper-tailed, lower-tailed, or two-tailed tests (as can be seen from the example above, the default is two-tailed).

Here are the one-tailed tests

Here is one with a different null hypothesis

The arguments `mu` and `alternative` are used similarly for two-sample tests.

## Power Calculations

### Normal Reference Distribution

These are the examples done in the slides for the class (slides 186–194, deck 2).

does the upper-tailed test and

does the two-tailed test.

The R functions `pnorm` and `qnorm` (on-line help) do the DF and inverse DF of the normal distribution.

The R keyword `for` (on-line help) indicates a loop. In this example, the first `curve` command draws the first power curve for sample size `n[1]`, and the second `curve` command draws the remaining power curves for sample sizes `n[2]`, through `n[length(n)]`.

The R function `curve` (on-line help) draws curves. In the first argument `x` is a free variable ranging between the values of the `from` and `to` arguments.

The (on-line help for topic plotmath) explains what

```    xlab = expression((theta - theta[0]) / tau)
```
does.

### Student T Reference Distribution

These are the examples done in the slides for the class (slides 195–201, deck 2).

does the upper-tailed test and

does the two-tailed test.

The R functions `pt` and `qt` (on-line help) do the DF and inverse DF of the t distribution.