Let Y1, Y2, . . . , Y20 be a random sample of size n =...

Let Y1, Y2, . . . , Y20 be a random sample of size n = 20 from a normal distribution with unknown mean µ and known variance σ 2 = 5. We want to test H0; µ = 7 vs. Ha : µ > 7. (a) Find the uniformly most powerful test with significance level 0.05. (b) For the test in (a), find the power at each of the following alternative values of µ: µa = 7.5, 8.0, 8.5, and 9.0. (c) Sketch a graph of the power function (d) What is the smallest sample size n such that an α = 0.05-level test has power at least 0.8 when µ = 8?

Expert Solution

orchestra answered 2 years ago

Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample...

Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample of size n = 4 from a distribution with pdf f(x) = 3X2, 0 < x < 1, zero elsewhere. (a) Find the joint pdf of Y3 and Y4. (b) Find the conditional pdf of Y3, given Y4 = y4. (c) Evaluate E(Y3|y4)

Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on...

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Let Y1, Y2, ..., Yn be a random sample from an exponential distribution with mean theta....

Let Y1, Y2, ..., Yn be a random sample from an exponential distribution with mean theta. We would like to test H0: theta = 3 against Ha: theta = 5 based on this random sample. (a) Find the form of the most powerful rejection region. (b) Suppose n = 12. Find the MP rejection region of level 0.1. (c) Is the rejection region in (b) the uniformly most powerful rejection region of level 0.1 for testing H0: theta = 3...

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Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a)...

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Let Y1,Y2,...,Yn be a Bernoulli distributed random sample with P(Yi = 1) = p and P(Yi...

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Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2...

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Let X1, X2, . . . , Xn be a random sample of size n from...

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