Sprott and Farewell (1993) note that in the two-sample t test, a valid t statistic can be derived as long as the ratio of variances is known. Let X1,..., Xn1 be a sample from a n(μ1, σ2) and Y1,..., Yn2 a sample from a n(μ2, p2σ2), where p2 is known. Show that

Sprott and Farewell also note that the t statistic is maximized at

and they suggest plotting the statistic for plausible values of p2, possibly those in a confidence interval.

n2 1 n2