We have 10 observations, 0.6377,1.9339,−2.1588,0.9622,0.4188,−1.2077,−0.3336,0.4426,3.6784,2.8694, from a Gaussian distributionN(μ,1).
Test whether μ= 0.5 at the 5% level.
We have 10 observations, 0.6377,1.9339,−2.1588,0.9622,0.4188,−1.2077,−0.3336,0.4426,3.6784,2.8694, from a Gaussian distributionN(μ,1). Test whether μ= 0.5 at the 5%...
2. Suppose that we have 9 independent observations from a normal distribution with standard deviation 10. We wish to test Ho : μ-150 vs. H A : μ 150 The best test with level a- 0.05 uses the test statistic T1 =1元-1501 and has a critical value of c 6.53. The test rejects the null hypothesis when T> c (a) Calculate the power of this test against the alternative μ-151. (b) Calculate the power of this test against the alternative...
We are looking to calculate the power of a one-sided test from n independent observations from a N(μ, σ2) distribution with a null hypothesis of Ho : μ-μο and an alternative H1 : μ > μο. Supposing that we know σ2, we can form a test statistic o/Vn and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power of this test against the alternative that μ-A-This power...
6. We are given 5 observations, namely (-51.2, 42.88,-35.15, 41.04, -13.68] for the surface temperatures on an asteroid. We will assume that these are independent observations from a N(μ, σ*) distribution with given standard deviation σ-49. Suppose further that we have a prior distribution on μ that is Normal with m ean 0 and standard deviation 36. (a) Find the posterior distribution of μ, and the Bayes estimate of μ, the mean surface temperature. (b) Give a 96% Highest Posterior...
We are looking to calculate the power of a one-sided test from n independent observations Xi from a N(μ, σ2) distribution with a null hypothesis of Ho : μ-μ0 and an alternative H, : μ 〉 μ0. Supposing that we know σ2, we can form a test statistic T= and reject the null hypothesis when T 〉 1.645. This test has level α 0.05. We want a formula for the power of this test against the alternative that μ-74-This power...
In a test of the hypothesis H0: μ=10 versus Ha: μ≠10 a sample of =50 observations possessed mean overbar x=10.6 and standard deviation s=2.6 Find and interpret the p-value for this test The p-value for this test is __________. (Round to four decimal places as needed.) Interpret the result. Choose the correct answer below. A. There is sufficient evidence to reject H0 for α > 0.11. B.There is insufficient evidence to reject H0 for α=0.15. C.There is sufficient evidence to...
(16 points) Suppose the breaking strength of plastic bags is a Gaussian random variable Bags from company i have a mean strength of 8 kilograms and a variance of 1 kg2; Bags from company 2 have a mean strength of 9 kilograms and a variance of 0.5 kg' Assume we check the sample mean X1o of the breaking strength of 10 bags, and use X1o to determine whether a batch of bags comes from company 1 (null hypothesis Ho) or...
4. Setup: Suppose you have observations X1,X2,X3,X4,X5 which are i.i.d. draws from a Gaussian distribution with unknown mean μ and unknown variance σ2. Given Facts: You are given the following: 15∑i=15Xi=0.90,15∑i=15X2i=1.31 Bookmark this page Setup: Suppose you have observations X1, X2, X3, X4, X5 which are i.i.d. draws from a Gaussian distribution with unknown mean u and unknown variance o? Given Facts: You are given the following: x=030, =1:1 Choose a test 1 point possible (graded, results hidden) To test...
The rejection region for a 5% level test of H0 : μ ≥ 10 versus H1 : μ < 10 is X¯ < 7.8. Find the rejection region for a 1% level test.
The rejection region for a 5% level test of H0 : μ ≥ 10 versus H1 : μ < 10 is X¯ < 7.8. Find the rejection region for a 1% level test.
Thank you so much! 5. We have two independent samples of n observations X1,Xy,.. . ,x, and Y. Ya, . … We want to test the hypothesis Ho : μ,-μυ versus the alternative Hi : μ, μν. (a) First, assume that the null hypothesis Ho is true and find the MLE for μ (b) Then plug this estimate into the log likelihood along with the MLE μ'.. and 1,-j) to calculate the LRT statistic. (e) Is this likelihood ratio test...