# Question: Let X1 X2 Xn be a

Let X1, X2, . . . , Xn be a random sample of size n from the normal distribution N(μ, σ02), where σ02 is known but μ is unknown.

(a) Find the likelihood ratio test for H0: μ = μ0 against H1: μ ≠ μ0. Show that this critical region for a test with significance level α is given by |− μ0| > zα/2σ0/√n.

(b) Test H0: μ = 59 against H1: μ ≠ 59 when σ2 = 225 and a sample of size n = 100 yielded = 56.13. Let α = 0.05.

(c) What is the p-value of this test? Note that H1 is a two-sided alternative.

(a) Find the likelihood ratio test for H0: μ = μ0 against H1: μ ≠ μ0. Show that this critical region for a test with significance level α is given by |− μ0| > zα/2σ0/√n.

(b) Test H0: μ = 59 against H1: μ ≠ 59 when σ2 = 225 and a sample of size n = 100 yielded = 56.13. Let α = 0.05.

(c) What is the p-value of this test? Note that H1 is a two-sided alternative.

## Answer to relevant Questions

To test H0: μ = 335 against H1: μ < 335 under normal assumptions, a random sample of size 17 yielded = 324.8 and s = 40. Is H0 accepted at an α = 0.10 significance level? It has been claimed that, for a penny minted in 1999 or earlier, the probability of observing heads upon spinning the penny is p = 0.30. Three students got together, and they would each spin a penny and record the number X ...A student who uses a certain college’s recreational facilities was interested in whether there is a difference between the facilities used by men and those used by women. Use α = 0.05 and the following data to test the ...With a = 3 and b = 4, find μ, αi, and βj if μij, i = 1, 2, 3 and j = 1, 2, 3, 4, are given by In an “additive” model such as this one, one row (column) can be determined by adding a constant value to each of the ...By squaring the binomial expression [(Yi −) − (SxY/s2x)(xi − )], show thatPost your question