There seems to be a lot of interest in Likert scales of late. Such scales (order of preference among 1, 2,..,5, etc.) produce data that should be considered as ordered categorical. If comparing two or more data sets of this type across nominal categories (like gender), then rank procedures should be used.
If comparing across levels of another ordered variable (such as grade level), procedures for measuring association between ordered categorical variables should be used. The best ones involve concordant and discordant pairs, which are not difficult to count but which are not mentioned in introductory courses. (Perhaps they should be.)
If used as the response variable in a regression setting, then logistic regression can be employed. In the regression setting, treating the ordinal categories as continuous measurements is not too bad as long as there are at least 5 scale levels and a reasonable amount of data.
In short, it is not a good idea to use Likert scale data for illustrating the basic procedures covered in an introductory course. Even the chi-square test yields very little information here (as has been pointed out) since it tests only for overall association and not directions or strengths of possibly interesting specific associations.