## 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 `H`_{0} 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.

#### Comments

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.

#### Comments

The R functions `pt`

and `qt`

(on-line
help) do the DF and inverse DF of the `t` distribution.