Question

Suppose X is a single observation from a Beta(θ, 1) distribution, and consider the hypotheses H0...

Suppose X is a single observation from a Beta(θ, 1) distribution, and consider the hypotheses H0 : θ ≥ 2 vs H1 : θ < 2.

(a) Consider the test with rejection region R = {X < c}. Derive the power function of this test (as a function of θ and c).

(b) Find the value of c so that the test has size α = 0.01.

(c) Find the probability of a Type II error when θ = 1.

(d) If the observed data is x = 0.2, what is the corresponding p-value?

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.
Let X1, . . . , Xn ∼ iid Beta(θ, 1). (a) Find the UMP test...
Let X1, . . . , Xn ∼ iid Beta(θ, 1). (a) Find the UMP test for H0 : θ ≥ θ0 vs H1 : θ < θ0. (b) Find the corresponding Wald test. (c) How do these tests compare and which would you prefer?
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 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....
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.
Consider the hypotheses shown below. Given that x?=42 , ?=11 , n=31 , ?=0.01. H0: ??39...
Consider the hypotheses shown below. Given that x?=42 , ?=11 , n=31 , ?=0.01. H0: ??39 H1: ?>39 A. What conclusion should be drawn (z-test statistic)? B. Determine the P-value for this test.
1. In testing a null hypothesis H0 versus an alternative Ha, H0 is ALWAYS rejected if...
1. In testing a null hypothesis H0 versus an alternative Ha, H0 is ALWAYS rejected if A. at least one sample observation falls in the non-rejection region. B. the test statistic value is less than the critical value. C. p-value ≥ α where α is the level of significance. 1 D. p-value < α where α is the level of significance. 2. In testing a null hypothesis H0 : µ = 0 vs H0 : µ > 0, suppose Z...
9. In a test of hypotheses of the form ?0 : μ = 78.3 versus H1...
9. In a test of hypotheses of the form ?0 : μ = 78.3 versus H1 : μ ≠78.3 using ? = .01, when the sample size is 28 and the population is normal but with unknown standard deviation the rejection region will be the interval or union of intervals: (a) [2.771, ∞) (b) [2.473, ∞) (c) [2.576, ∞) (d) (−∞,−2.771] ∪ [2.771, ∞) (e) (−∞,−2.473] ∪ [2.473, ∞) 10. In a test of hypotheses ?0: μ = 2380 versus...
Suppose that we are to conduct the following hypothesis test: H0: μ=990 H1:μ>990 Suppose that you...
Suppose that we are to conduct the following hypothesis test: H0: μ=990 H1:μ>990 Suppose that you also know that σ=220, n=100, x¯=1031.8, and take α=0.01. Draw the sampling distribution, and use it to determine each of the following: A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a) is expressed (-infty, a), an answer of the form (b,∞) is expressed (b, infty), and an answer...
Suppose that we are to conduct the following hypothesis test: H0:H1:μμ=>10701070 Suppose that you also know...
Suppose that we are to conduct the following hypothesis test: H0:H1:μμ=>10701070 Suppose that you also know that σ=150, n=90, x¯=1101.5, and take α=0.01. Draw the sampling distribution, and use it to determine each of the following: A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a) is expressed (-infty, a), an answer of the form (b,∞) is expressed (b, infty), and an answer of the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT