Work out the following statistics questions
4. What is the rejection point (the number that cuts off the rejection region) for the significance level of .10 for a right-tail Z-based hypothesis test? 5. What is the rejection point (the number that cuts off the rejection region) for the significance level of .05 for a right-tail Z-based hypothesis test? 6. What is the rejection point (the number that cuts off the rejection region) for the significance level of .01 for a right-tail Z-based hypothesis test? 7. What is the rejection point (the number that cuts off the rejection region) for the significance level of . 10 for a left-tail Z-based hypothesis test? 8. What is the rejection point (the number that cuts off the rejection region) for the significance level of .05 for a left-tail Z-based hypothesis test?| 9. What is the rejection point (the number that cuts off the rejection region) for the significance level of .01 for a left-tail Z-based hypothesis test? 10. What is the rejection point (the number that cuts off the rejection region) for the significance level of .10 for a two-tail Z-based hypothesis test? 11. What is the rejection point (the number that cuts off the rejection region) for the significance level of .05 for a two-tail Z-based hypothesis test? 12. What is the rejection point (the number that cuts off the rejection region) for the significance level of .01 for a two-tail Z-based hypothesis test?Problem 2 [3 + 3 + 3 + 3 = 12 points] Consider a Markov chain with three states {31,312, 33}, and the following transition matrix: 1/2 1/2 0 A: 0 1/3 2/3 2/3 0 1/3 1) Draw the state diagram, annotated with transition probabilities for Markov chain. 2) Given that the initial distribution on = (1,010), what is the probability that the chain is in state 32 after 2 steps. 3) Find the steady state distribution for this Markov chain. 4) Suppose that when you visit state 5 you receive f(s) dollars where f[s.) = l, f(.5'2) = 2, and ffsg] = 3. What's the value of E(f(X2))? (Note that X; is the random variable of the states at time step 2. X0 is the random variable of the states at time step 0.) 7.2 The Central Limit Theorem for Sums 1. Central limit theorem for means {X}: 3. The condition for central limit theorem I The sample size should be at least .................... or the sample data should come from a if the sample size is :5 30, then X has a normal distribution even if the data values (X) of the population do not follow a normal distribution. 4. Suppose that A C B C R and that both sets are nonempty and bounded. Prove that inf A
