Let x and y denote the weights in grams of male and female gallinules, respectively. assume that x is $n(\mu_x, \sigma^2_x)$ and y is $n(\mu_y, \sigma^2_y)$. suppose there are n = 16 observations of x and m = 13 observations of y. we are interested in testing the null hypothesis $h_0: \mu_x=\mu_y $ against the one-sided alternative hypothesis $h_1: \mu_x > \mu_y $. let $\alpha = 0.01$.(assume that the variances are equal.)

let us say we suspect that that equality is not valid. thus, use the test proposed by welch.

what is the value of welch's test statistic?