PROBLEM 2E

(In some of the exercises that follow, we must make assumptions such as the existence of normal distributions with equal variances.)

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, 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 hypothesisH1: μX > μY. Let α = 0.01. (Assume that the variances are equal.)

(b) Given that and s2y= 692.21, calculate the value of the test statistic and state your conclusion.

(c) Although we assumed that σ2 X = σ2Y , let us say we suspect that that equality is not valid. Thus, use the test proposed by Welch.

Erika Halloway Project 3 Secretary Notes Kate Ericson – Pyramid and Greek Buildings –Afeel of an archelogical dig –Contrast in size and apperance –Pyramid: apperance of perfection vs. Greek building: crumbling, more worn out –Interior space is open –Hole: Portal of sort to an hidden culture –Indiana Jones feel Emily Gaustae –Doll house-like look and effect –Structure is complex and not quite symmetrical –Years on the tree; 2–4 year gap –Tree represents growth