Let X and Y denote the weights in grams of male and female common gallinules, respectively. Assume that X is N(µX, σ2 X) and Y is N(µY , σ2 Y ). a. Given n = 16 observations of X and m = 13...

Let X and Y denote the weights in grams of male and female common gallinules, respectively. Assume that X is N(µX, σ2 X) and Y is N(µY , σ2 Y ). a. Given n = 16 observations of X and m = 13 observations of Y, find a test statistic and a critical region for testing the null hypothesis H0: µX = µY against the one sided alternative hypothesis Ha : µX > µY . Let α = 0.01. (assume that the variances are equal). b. Given that ¯x = 415.16, s2 x = 1356.75, y¯ = 347.40, and s 2 y = 692.21, calculate the value of the test statistic and state your conclusion.