Let X and Y denote the weights in grams of male and female common gallinules, respectively Assume that X is N(X, 2x) and Y is N(Y, 2Y) (a) Given n 16 observations of X and m 13 observations of Y, define a test statistic and a critical region for testing the null hypothesis H0 X Y against the one si...

a b t 41516 34740 15 135675 126922127116 113 5570 2473 ...

Let X and Y denote the weights in grams of male and female common gallinules, respectively. Assume

Question:

Let X and Y denote the weights in grams of male and female common gallinules, respectively. Assume that X is N(μX, σ2x) and Y is N(μY, σ2Y).
(a) Given n = 16 observations of X and m = 13 observations of Y, define a test statistic and a critical region for testing the null hypothesis H0: μX = μY against the one-sided alternative hypothesis H1: μX > μY. Let α = 0.01. (Assume that the variances are equal.)
(b) Given that = 415.16, s2x = 1356.75, = 347.40, and s2y = 692.21, calculate the value of the test statistic and state your conclusion.
(c) Although we assumed that σ2x = σ2Y, let us say we suspect that that equality is not valid. Thus, use the test proposed by Welch