Question

Suppose Y ~ N(u, 1) is a single observation from the normal density. Consider the test...

Suppose Y ~ N(u, 1) is a single observation from the normal density. Consider the test H0: u = 0 and H1: u = 1.

Find the most powerful test of size alpha = 0.05.

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
Suppose Y ~ N(u,1) is a single observation from the normal density. Consider the test H0:...
Suppose Y ~ N(u,1) is a single observation from the normal density. Consider the test H0: u = 0 and H1: u = 1. Find the most powerful test of size alpha = 0.05 and find the probability of Type II error from this test. Also, find the test that minimizes the sum of the two error probabilities.
Consider the following hypothesis test: H0:u equal to 25 H1: u> 25 α=0.05, σ= 2.4,n=30 what...
Consider the following hypothesis test: H0:u equal to 25 H1: u> 25 α=0.05, σ= 2.4,n=30 what would be the cutoff value for y mean for the rejection of h0? If the true value is u=25.75, then what is the power of the test?
Suppose we observe Y1,...Yn from a normal distribution with unknown parameters such that ¯ Y =...
Suppose we observe Y1,...Yn from a normal distribution with unknown parameters such that ¯ Y = 24, s2 = 36, and n = 15. (a) Find the rejection region of a level α = 0.05 test of H0 : µ = 20 vs. H1 : µ 6= 20. Would this test reject with the given data? (b) Find the rejection region of a level α = 0.05 test of H0 : µ ≤ 20 vs. H1 : µ > 20....
1. (a) Y1,Y2,...,Yn form a random sample from a probability distribution with cumulative distribution function FY...
1. (a) Y1,Y2,...,Yn form a random sample from a probability distribution with cumulative distribution function FY (y) and probability density function fY (y). Let Y(1) = min{Y1,Y2,...,Yn}. Write the cumulative distribution function for Y(1) in terms of FY (y) and hence show that the probability density function for Y(1) is fY(1)(y) = n{1−FY (y)}n−1fY (y). [8 marks] (b) An engineering system consists of 5 components connected in series, so, if one components fails, the system fails. The lifetimes (measured in...
3. Let Y be a singleobservation from a population with density function. f(y)=  2y/θ2 0 ≤ y...
3. Let Y be a singleobservation from a population with density function. f(y)=  2y/θ2 0 ≤ y ≤ θ   f(y)=  0     elsewhere (d) Use the pivotal Y /θ to find a 100(1 − α)% upper confidence interval for θ, which is of form (−∞, θˆU ). For the following questions, suppose for some θ0 > 0, we wish to test H0 :θ = θ0v.s. H1 :θ < θ0 based on a single observation Y . (e) Show that a level-α test has the...
Suppose you want to test H0: u <=100 against H1: u> 100 using a significance level...
Suppose you want to test H0: u <=100 against H1: u> 100 using a significance level of 0.05. The population is normally distributed with a standard deviation of 75. A random sample size of n = 40 will be used. If u = 130, what is the probability of correctly rejecting a false null hypothesis? What is the probability that the test will incorrectly fail to reject a false null hypothesis?
Consider the test of H0: varience = 15 against H1: variance > 15. What is the...
Consider the test of H0: varience = 15 against H1: variance > 15. What is the critical value for the test statistic chi-square for the significance level alpha = 0.05 and sample size n = 18
Y is a random variable pdf h(y) = (1/(y+ theta)^3) * 2 * theta^2 y >0,...
Y is a random variable pdf h(y) = (1/(y+ theta)^3) * 2 * theta^2 y >0, theta >0 Using a single observation, test H_0 : Theta = 1 H_a : theta > 1 Find a uniformly most power critical region for test if alpha = .05 Then find the power of test if theta = 2.5
You have an SRS of size n = 10 from a Normal distribution with s =...
You have an SRS of size n = 10 from a Normal distribution with s = 1.1. You wish to test H0: µ = 0 Ha: µ > 0 You decide to reject H0 if x > 0.05 and to accept H0 otherwise. Find the probability (±0.1) of a Type I error. That is, find the probability that the test rejects H0 when in fact µ = 0: _____ Find the probability (±0.001) of a Type II error when µ...
Consider a sample of a normal distribution of size n = 20. Test the Hypothesis Ho:...
Consider a sample of a normal distribution of size n = 20. Test the Hypothesis Ho: μ = 300 vs Ha: μ ≠ 300 with alpha 0.05 283 345 372 302 312 318 295 376 350 333 301 287 334 326 373 261 302 326 380 313
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT