Suppose y1, ... yn ~ iid N(0, sigma^2), Ho: sigma = sigma0 Ha: sigma = sigma1. ...

Suppose y1, ... yn ~ iid N(0, sigma^2),

Ho: sigma = sigma0
Ha: sigma = sigma1. where sigma0 < sigma1

Test rejects Ho when T(y) = Sum(yi^2) is large.

Find rejection region for the test for a specified level of alpha

Expert Solution

orchestra answered 1 year ago

Construct a two-sided (1−α)-CI for θ in Uniform[0,θ] based on IID Y1,...,Yn

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and...

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and Y1...Xn independent of each other. Assume that the common population SD σ is known but the two means are not. Consider testing the hypothesis null: μx = μy vs alternative: μx ≠ μy. d. Assume σ=1 and n=20. How large must δ be for the size 0.01 test to have power at least 0.99? e. Assume σ=1and δ=0.2. How large must n be for...

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and...

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and Y1...Xn independent of each other. Assume that the common population SD σ is known but the two means are not. Consider testing the hypothesis null: μx = μy vs alternative: μx ≠ μy. a. Find the likelihood ratio test statistic Λ. Specify which MLEs you are using and how you plug them in.

Please show work and explain steps Assume Y1, ... , Yn are IID continuous variables with...

*Please show work and explain steps* Assume Y1, ... , Yn are IID continuous variables with PDF f(yi; θ), where f is dependent on a parameter θ. Complete the following: a) Derive the likelihood, L(θ), and the log-likelihood, l(θ), in terms of the function f. b) Find dl/d(theta) in terms of f(yi; θ) and df/d(theta). Note that dl/d(θ) is usually referred to as the score function. c) Show that E[dl/d(θ)]= 0. Hint: you can use without proof the following: ∫...

Suppose that the random variable Y1,...,Yn satisfy Yi = ?xi + ?i i=1,...,n. where the set...

Suppose that the random variable Y1,...,Yn satisfy Yi = ?xi + ?i i=1,...,n. where the set of xi are fixed constants and ?i are iid random variables following a normal distributions of mean zero and variance ?2. ?a (with a hat on it) = ?i=1nYi xi / ?i=1nx2i is unbiased estimator for ?. The variance is ?a (with a hat on it) = ?2/ ?i=1nx2i . What is the distribation of this variance?

Let Y1, ... , Yn be a random sample that follows normal distribution N(μ,2σ^2) i)get the...

Let Y1, ... , Yn be a random sample that follows normal distribution N(μ,2σ^2) i)get the mle for σ^2 ii)prove using i) that it is an efficient estimator

Suppose that Y1 ,Y2 ,...,Yn is a random sample from distribution Uniform[0,2]. Let Y(n) and Y(1)...

Suppose that Y1 ,Y2 ,...,Yn is a random sample from distribution Uniform[0,2]. Let Y(n) and Y(1) be the order statistics. (a) Find E(Y(1)) (b) Find the density of (Y(n) − 1)2 (c) Find the density of Y(n) − Y (1)

Given Ho = M ≥ 45 n = 36 ∞ = 2.0 Ha = M...

Given Ho = M ≥ 45 n = 36 ∞ = 2.0 Ha = M < 45 ẋ = 48 At ∞ = 0.01 do we reject or fail to reject Ho

Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent random samples, with...

Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent random samples, with the variables Xi normally distributed with mean μ1 and variance σ12 and the variables Yi normally distributed with mean μ2 and variance σ22. The difference between the sample means, X − Y, is then a linear combination of m + n normally distributed random variables and, by this theorem, is itself normally distributed. (a) Find E(X − Y). (b) Find V(X − Y). (c)...

Suppose Y1, . . . , Yn are independent random variables with common density fY(y) =...

Suppose Y1, . . . , Yn are independent random variables with common density fY(y) = eμ−y y > μ. Derive a 95% confidence interval for μ. Find the MLE for μ to use as the estimator

Question

Suppose y1, ... yn ~ iid N(0, sigma^2), Ho: sigma = sigma0 Ha: sigma = sigma1. ...

Solutions

Expert Solution

Related Solutions

Construct a two-sided (1−α)-CI for θ in Uniform[0,θ] based on IID Y1,...,Yn

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and...

3. Let X1...Xn be N(μX,σ) and Y1...Yn be iid N(μy,σ) with the two samples X1...Xn, and...

Please show work and explain steps Assume Y1, ... , Yn are IID continuous variables with...

Suppose that the random variable Y1,...,Yn satisfy Yi = ?xi + ?i i=1,...,n. where the set...

Let Y1, ... , Yn be a random sample that follows normal distribution N(μ,2σ^2) i)get the...

Suppose that Y1 ,Y2 ,...,Yn is a random sample from distribution Uniform[0,2]. Let Y(n) and Y(1)...

Given Ho = M ≥ 45 n = 36 ∞ = 2.0 Ha = M...

Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent random samples, with...

Suppose Y1, . . . , Yn are independent random variables with common density fY(y) =...