I would also like to know why the supremum occurs at theta 1/2 along with the solutions to part a,b and c.
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I would also like to know why the supremum occurs at theta 1/2
along with the...
Suppose Xi and X2 are iid from 0, otherwise, where θ 0, and consider testing Ho : θ 1 versus H1 :...
Suppose Xi and X2 are iid from 0, otherwise, where θ 0, and consider testing Ho : θ 1 versus H1 : θ 1 . We have two tests: where 0<c<1 (a) Show that the power functions of the two tests are A(0)-1-(0.9)θ and β2(0)-1 + d|θ Inc-1), respectively. (b) Calculate the size of the φι test. Then, find the value of c that gives the same size for the φ2 test. (c) Is фг a most powerful test of...
I would like the whole Question done on r studio with the R Code. 1. In...
I would like the whole Question done on r studio with
the R Code.
1. In this question we will evaluate type I and type II error probabilities for one-sided tests. We will consider normally distributed data, with unit variance and independent obervations. We will use Ho : μ-0 for the null and H1 : μ-1 for the alternative, unless otherwise stated. (a) Suppose we have n-6 observationsx. What is the sampling distribution of the (10 marks) sample mean (that...
Suppose that X1, X2,..., Xn are iid from where a 1 is a known constant and...
Suppose that X1, X2,..., Xn are iid from where a 1 is a known constant and θ > 0 is an unknown parameter. (a) Show that the likelihood ratio rejection region for testing Ho : θ θο versus H : θ > θο can be written in terms of X(n), the maximum order statistic. (b) Derive the power function of the test in part (a). (c) Derive the most powerful (MP) level α test of Ho : θ-5 versus H1...
Let X 1, X 2, X 3, X 4 be a random sample of size n=4...
Let X 1, X 2, X 3, X 4 be a random sample of size n=4 from a Poisson distribution with mean . We wish to test Ho: I = 3 vs. H1: \<3. a) Find the best rejection region with the significance level a closest to 0.05. Hint 1: Since H1: X< 3, Reject Ho if X 1+X 2 +X 3 +X 4<= 0 Hint 2: X 1+X 2 +X 3 + X 4 ~ Poisson (4) Hint 3:...
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution...
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution with mean ?. Consider the test Ho : ?-2.6 vs. H 1 : ? < 2.6. a)Find the best rejection region with the significance level a closest to 0.10 b) Find the power of the test from part (a) at ?= 2.0 and at ?=1.4. c) Suppose x1-1, x2-2, x3 -0, x4-1, x5-2. Find the p-value of the test.
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the...
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the alternative hypothesis H1 0 2 Denote by C aat the critical region of a test at the significance level of : α-0.05. (f [2 marks] Show that the test is also the uniformly most powerful (UMP) test when the alternative hypothesis is replaced with H1 0 > 1 (g) [2 marks Show...
Please answer all parts, use question #2 to solve #3. 2. For a random sample of...
Please answer all parts, use question #2 to solve #3.
2. For a random sample of size n = 25, the correlation is r = 0.31 for normal random variables X and Y. Answer the questions for the hypothesis test. Use a level of significance of a = 0.08. Ho: p= 0 H1: p0 a. The critical value is Z = b. The test statistic is Z = C. The p-value is d. The hypothesis (should, should not) be rejected....
1 versus H:λ 2. Find a 6. Consider Neyman-Pearson Lemma. Consider testing Ho:λ suitable number k ...
1 versus H:λ 2. Find a 6. Consider Neyman-Pearson Lemma. Consider testing Ho:λ suitable number k so that this lemma can be applied. Do you see any change in k if we replace 1 and 2 above by 4 and 51 our X is still Poisson from number 5; choose any meaningful alpha for number 6 and do the problem.) (Question 5. For the random variable X following a Poisson distribution with mean 2 Consider testing Ho: λ 1 versus...
please answer all parts in detail! :) 4. Suppose the weights of parts in one lot...
please answer all parts in detail! :)
4. Suppose the weights of parts in one lot has a normal distribution. Six parts were randomly drawn from this lot and weighed. Their weights were 21.6 oz. 22.4 oz. 21.4 oz. 20.2 oz. 22.0 oz 20.8 oz The sample mean x= 21.4 oz and sample standard deviation s = 0.8 oz. (a) (1 point] Calculate the test statistic for testing Ho: u = 22 oz, where u = 22 oz is the...
Suppose Xi and X2 are iid from 0, otherwise, where θ 0, and consider testing Ho : θ 1 versus H1 : θ 1 . We have two tests: where 0<c<1 (a) Show that the power functions of the two tests are A(0)-1-(0.9)θ and β2(0)-1 + d|θ Inc-1), respectively. (b) Calculate the size of the φι test. Then, find the value of c that gives the same size for the φ2 test. (c) Is фг a most powerful test of...
I would like the whole Question done on r studio with
the R Code.
1. In this question we will evaluate type I and type II error probabilities for one-sided tests. We will consider normally distributed data, with unit variance and independent obervations. We will use Ho : μ-0 for the null and H1 : μ-1 for the alternative, unless otherwise stated. (a) Suppose we have n-6 observationsx. What is the sampling distribution of the (10 marks) sample mean (that...
Suppose that X1, X2,..., Xn are iid from where a 1 is a known constant and θ > 0 is an unknown parameter. (a) Show that the likelihood ratio rejection region for testing Ho : θ θο versus H : θ > θο can be written in terms of X(n), the maximum order statistic. (b) Derive the power function of the test in part (a). (c) Derive the most powerful (MP) level α test of Ho : θ-5 versus H1...
Let X 1, X 2, X 3, X 4 be a random sample of size n=4 from a Poisson distribution with mean . We wish to test Ho: I = 3 vs. H1: \<3. a) Find the best rejection region with the significance level a closest to 0.05. Hint 1: Since H1: X< 3, Reject Ho if X 1+X 2 +X 3 +X 4<= 0 Hint 2: X 1+X 2 +X 3 + X 4 ~ Poisson (4) Hint 3:...
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution with mean ?. Consider the test Ho : ?-2.6 vs. H 1 : ? < 2.6. a)Find the best rejection region with the significance level a closest to 0.10 b) Find the power of the test from part (a) at ?= 2.0 and at ?=1.4. c) Suppose x1-1, x2-2, x3 -0, x4-1, x5-2. Find the p-value of the test.
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the alternative hypothesis H1 0 2 Denote by C aat the critical region of a test at the significance level of : α-0.05. (f [2 marks] Show that the test is also the uniformly most powerful (UMP) test when the alternative hypothesis is replaced with H1 0 > 1 (g) [2 marks Show...
Please answer all parts, use question #2 to solve #3.
2. For a random sample of size n = 25, the correlation is r = 0.31 for normal random variables X and Y. Answer the questions for the hypothesis test. Use a level of significance of a = 0.08. Ho: p= 0 H1: p0 a. The critical value is Z = b. The test statistic is Z = C. The p-value is d. The hypothesis (should, should not) be rejected....
1 versus H:λ 2. Find a 6. Consider Neyman-Pearson Lemma. Consider testing Ho:λ suitable number k so that this lemma can be applied. Do you see any change in k if we replace 1 and 2 above by 4 and 51 our X is still Poisson from number 5; choose any meaningful alpha for number 6 and do the problem.) (Question 5. For the random variable X following a Poisson distribution with mean 2 Consider testing Ho: λ 1 versus...
please answer all parts in detail! :)
4. Suppose the weights of parts in one lot has a normal distribution. Six parts were randomly drawn from this lot and weighed. Their weights were 21.6 oz. 22.4 oz. 21.4 oz. 20.2 oz. 22.0 oz 20.8 oz The sample mean x= 21.4 oz and sample standard deviation s = 0.8 oz. (a) (1 point] Calculate the test statistic for testing Ho: u = 22 oz, where u = 22 oz is the...
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