Let X : N (4, o2)Vi = 1, 2, 3, ... 50 for tenting H : µ = 1 0. against H, : H = 2 if x 22 is the critical region then find the two types of errors and power of test.
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Let X 1 ,X 2 ,...,X n be a r.s. of size n from a distribution N(theta, 1) find best critical region of size a for testing H 0 : theta=0 against H 1 : theta=1 , also find the value of c if n = 25 and a = 5%.Z= 6.35 Determine the critical value (z) of the rejection region, assuming a 5% level of significance
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- Suppose that (X,Y) is uniformly distributed over the region {(x,y): 0 < |y| < x < 1}. Find E(X) and E(Y).Suppose that X and Y are independent measurement of a quantity μ. E(X) = E(Y) = μ, σX ≠ σY, Z = αX + (1 - α)Y, α ∈ [0, 1] (a) Show that E(X) = μ. (b) Find α in terms of σX and σY to minimize V(Z). (c) Under what circumstance is it better to use the average (X+Y)/2 than either X or Y alone?If the exponent of e of a bivariate normal density is −154 (x2 + 4y2 + 2xy + 2x + 8y + 4)find σ1, σ2, and ρ, given that μ1 = 0 and μ2 = −1.
- integrate ƒ over the given region. ƒ(x, y) = 1/(xy) over the square 1<=x<= 2, 1 <=y<=2.Find the average value of f(x,y)= 4x+2y on the region bounded byx=0,y=0, and x + y= 3An education researcher claims that at most 3% of working college students are employed as teachers or teaching assistants. In a random sample of 600 working college students, 5% are employed as teachers or teaching assistants. At α=0.01, is there enough evidence to reject the researcher's claim? Complete parts (a) through (e) below. (a) Find the critical value(s) and identify the rejection region(s). Z0=_________ (b) Identify the critical value(s) for this test ________ A.) The rejection regions are z < ___and z > ____ B.) The rejection region is z > _______ C.) The rejection region is _____< z < _____ D.) The rejection region is z < _____ (c) Decide whether to reject or fail to reject the null hypothesis and (d) interpret the decision in the context of the original claim.