This is never done with nominal variables, and usually only with interval or ratio variables. A T Test is a test of statistical significance and is used to determine whether or not to reject the null hypothesis. A T distribution is used to determine the level of statistical significance of an observed difference between sample means. When the .10 level is chosen there is one chance in 10 that you will reject the null when in fact it is correct. Power is the probability that a particular test of significance will lead to the rejection of a false null.
Power increases automatically with sample size.
The larger the sample the smaller the difference or relationship needed to reject the null. Takes means from numerous samples of the population. The more you take the narrower the dispersion of the means. See below for formula.