Unequal Variances
The … test can be extended to a problem in which the variances of the two normal distributions are not equal, but the ratio of one variance to the other is known. Specifically, suppose that … form a random sample from a normal distribution with mean … and variance … , and … form an independent random sample from another normal distribution with mean … and variance … Suppose also that the values of … , and … are unknown but that … , where … is a known positive constant. Then it can be shown (See Exercise 4 at the end of this section) that when …