Solve for the roots of the quadratic equation that defines Fieller's confidence set for the ratio of normal means (see Miscellanea 9.5.3). Find conditions on the random variables for which
a. The parabola opens upward (the confidence set is an interval).
b. The parabola opens downward (the confidence set is the complement of an interval).
c. The parabola has no real roots.
In each case, give an interpretation of the meaning of the confidence set. For example, what would you tell an experimenter if, for his data, the parabola had no real roots?