Question

Suppose X1, · · · , Xn from a normal distribution N(µ, σ2 ) where µ...

Suppose X1, · · · , Xn from a normal distribution N(µ, σ2 ) where µ is unknown but σ is known. Consider the following hypothesis testing problem:

H0 : µ = µ0 vs. Ha : µ > µ0

Prove that the decision rule is that we reject H0 if

X¯ − µ0 σ/√ n > Z(1 − α),

where α is the significant level, and show that this is equivalent to rejecting H0 if µ0 is less than the 100(1 − α)% lower confidence bound for µ.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Exercise 4. Suppose that X = (X1, · · · , Xn) is a random sample...
Exercise 4. Suppose that X = (X1, · · · , Xn) is a random sample from a normal distribution with unknown mean µ and known variance σ^2 . We wish to test the following hypotheses at the significance level α. Suppose the observed values are x1, · · · , xn. For each case, find the expression of the p-value, and state your decision rule based on the p-values a. H0 : µ = µ0 vs. Ha : µ...
X1, · · · Xn ~ iid N(µ, σ2 ) (a) Derive a 100(1 − α)%...
X1, · · · Xn ~ iid N(µ, σ2 ) (a) Derive a 100(1 − α)% confidence interval for σ2 when µ is unknown. (b) Derive a α−test for σ2 when H0 : σ2 = σ02  vs H1 : σ2 < σ02  Where σ02 > 0 and µ is unknown.
4. Suppose that we have X1, · · · Xn iid∼ N(µ, σ2 ) (a) Derive...
4. Suppose that we have X1, · · · Xn iid∼ N(µ, σ2 ) (a) Derive a 100(1 − α)% confidence interval for σ 2 when µ is unknown. (b) Derive a α−test for σ 2 when hypotheses is given as: H0 : σ^2 = σ^2sub0 vs H1 : σ^2 < σ^2sub0 . where σ 2 0 > 0 and µ is unknown. I am particularly struggling with b. Part a I could do.
If (x1, . . . , xn) is a sample from an N(μ0, σ2) distribution, where...
If (x1, . . . , xn) is a sample from an N(μ0, σ2) distribution, where σ2 > 0 is unknown and μ0 is known a.determine the MLE of σ2. b. show that the mle of σ2 is asymptotically normal
Suppose that X1,..Xn are iid N(0,σ2) where σ>0 is the unknown parameter. with preassigned α in...
Suppose that X1,..Xn are iid N(0,σ2) where σ>0 is the unknown parameter. with preassigned α in (0,1), derive a level α LR test for the null hypothesis H0: σ2 = σ02 against H1: σ2/=σ02 in the implementable form. (Hint: When is the function g(u) = ue1-u, u > 0 increasing? When is it decreasing? Is your test one-sided or two-sided?)
Suppose that X1,...,Xn are iid N(μ,σ2) where μ is unknown but σ is known.  μ>=2. Let z(μ)=μ3....
Suppose that X1,...,Xn are iid N(μ,σ2) where μ is unknown but σ is known.  μ>=2. Let z(μ)=μ3. Find an initial unbiased estimator T for z(μ). Next, derive the Rao-Blackwellized version of T.
Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with...
Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with -∞<μ<∞ and σ2 > 0. a. Develop a likelihood ratio test for H0: μ <= μ0 vs. H1: μ > μ0 b. Develop a likelihood ratio test for H0: μ >= μ0 vs. H1: μ < μ0
Let X1, X2, . . . , Xn be a random sample from the normal distribution...
Let X1, X2, . . . , Xn be a random sample from the normal distribution N(µ, 36). (a) Show that a uniformly most powerful critical region for testing H0 : µ = 50 against H1 : µ < 50 is given by C2 = {x : x ≤ c}. Find the values of c for α = 0.10.
Suppose that X1,..., Xn∼iid N(μ,σ2). a) Suppose that μ is known. What is the MLE of...
Suppose that X1,..., Xn∼iid N(μ,σ2). a) Suppose that μ is known. What is the MLE of σ? (b) Suppose that σ is known. What is the MLE of μ? (c) Suppose that σ is known, and μ has a prior distribution that is normal with known mean and variance μ0 and σ02. Find the posterior distribution of μ given the data.
Let X1, . . . , Xn ∼ iid N(θ, σ^2 ) for σ ^2 known....
Let X1, . . . , Xn ∼ iid N(θ, σ^2 ) for σ ^2 known. Find the UMP size-α test for H0 : θ ≥ θ0 vs H1 : θ < θ0.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT