1.In order to determine the average price of hotel rooms in Atlanta, a sample of 53 hotels were selected. It was determined that the test statistic (z) was $1.79. We would like to test whether or not the average room price is significantly different from $110. Population standard deviation is known to us.

Compute the p-value.

2.In order to determine the average price of hotel rooms in Atlanta. Using a 0.1 level of significance, we would like to test whether or not the average room price is significantly different from $110. The population standard deviation is known to be $16. A sample of 64 hotels was selected. The test statistic (z) is calculated and it is -1.67.

We conclude that the average price of hotel rooms in Atlanta is NOT significantly different from $110. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)

3.In order to determine the average price of hotel rooms in Atlanta. Using a 0.1 level of significance, we would like to test whether or not the average room price is significantly different from $110. The population standard deviation is known to be $16. A sample of 64 hotels was selected. The p-value associated with the test statistic (z) is calculated and it is 0.19.

We conclude that the average price of hotel rooms in Atlanta is NOT significantly different from $110. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)

4.A sample of 30 account balances of a credit company showed an average balance of $1,180 and a standard deviation of $125. You want to determine if the mean of all account balances is significantly greater than $1,150. Assume the population of account balances is normally distributed.

Compute the p-value for this test.

5.A sample of 28 account balances of a credit company was taken to test whether the mean of all account balances is significantly greater than $1,150. Using the sample standard deviation, the test statistic (t) was calculated to be $1.89. We use a 0.05 level of significance. Assume the population of account balances is normally distributed and the population standard deviation is unknown to us.

We conclude that the mean of all account balances is significantly greater than $1,150. (Enter 1 if the conclusion is correct. Enter 0 if the conclusion is wrong.)

1. What is the meaning of the central limit theorem for means, and the central limit theorem for proportions? When and how are they used? Compare and contrast the central limit theorem for means vs. the central limit theorem for proportions. Include at least one similarity, and one difference.Question 17 4 pts Which of the following statements is NOT consistent with the Central Limit Theorem? O The Central Limit Theorem indicates that the mean of the sampling distribution will be equal to the population mean. O The Central Limit Theorem indicates that the sampling distribution will be approximately normal when the sample size is sufficiently large. O The Central Limit Theorem applies to non-normal distributions. O The Central Limit Theorem applies without regard to the size of the sample.Question 2. (31] points) Consider a 3state Markov chain as shown in the state diagram in Figure 2, in which the reward of each state are 112(51): 1, R(52} : 3, and R{s3} : 1. 0.0 Figure 2: The 3state Markov chain diagram for lQuestion 2. {a} [15 points) Compute the values of each state, assmniug a discount factor of '7 = 0.9. {b} {15 points) Compute the values of each state with a discount factor of T : {1.1. Give your comments on the difference between the outcomes of Questions 2(a) and 2|[b]? Hint: For any state 5 anal policy 71' of a Markov chain with rewards, the state value function at a state 3 satises the following Bellman equation was) = Hts) + szs'lmcsn ms'), A stationary distribution of an m-state Markov chain is a probability vector q such that = q P, where P is the probability transition matrix. A Markov chain can have more than one stationary distribution. Identify all the stationary distributions that you can, for the 3-state Markov chain with transition probability matrix O O P Owl Does this Markov chain have a steady-state probability distribution ? 15 points