Attached Files:

Soda.xlsx (10.122 KB)

WebProfits.xlsx (94.367 KB)

Activity I - You have just opened a restaurant in a large city, and you are deciding what you should charge for a regular-sized soda. You'd like to charge a price equal to the average of your competitors, which you believe is $2.58. To inform your decision, you want to learn more about the average price charged by competing restaurants in the area. You know you won't be able to get prices for every restaurant, so you randomly sample 35 and collect their soda prices. These data are in Soda.xlsx (See the attached)

You are assuming the mean soda price is $2.58 for all of your competitors. When conducting data analysis to test this belief, what is this assumption called?

Calculate the t-statistic assuming the mean soda price for all of your competitors is $2.58.

Calculate the p-value for your t-statistic.

Using a confidence level of 90%, test whether the mean soda price of all your competitors is $2.58 using the t-stat.

Using a confidence level of 90%, test whether the mean soda price of all your competitors is $2.58 using the p-value.

Is it possible that your answers to parts d and e would yield different conclusions?

Activity II - To better assess your willingness-to-pay for advertising on others' websites, you want to learn the mean profit per visit for all visits to your website. To accomplish this, you have collected a random sample of 4,738 visits to your website over the past six months. This sample includes information on visit duration and profits. The data are contained in WebProfits.xlsx (See the attached) Using the data in WebProfits.xlsx:

Build a 99% confidence interval for the mean profit per visit for all of your visitors.

Let the null hypothesis be that mean profit per visit for all of your visitors is $11.50.

Calculate the corresponding t-stat for this null hypothesis.

Calculate the corresponding p-value for this null hypothesis.

With strength of 95%, decide whether or not to reject this null hypothesis.

Detail the reasoning behind your decision.

1. Consider the Markov chain with three states, S={1,2,3), that has the following transition matrix: 0.3 0.4 0.3 P = 0.1 0.3 0.6 0.1 0.2 0.7 with initial distribution mo =(0.2; 0.3; 0.5) . 1) Plot state transition diagram of the Markov Chain; 2) Find the Markov transition matrix after 2 steps; 3) Find the Markov Chain distribution after two steps; 4) Find the Markov chain realization: (X1=1; X2=2; X4=3 ; X7=2) 5) Find the stationary distribution of the Markov Chain - (co).Can the Gauss-Markov Theorem be used to rank the variances of the OLS estimator and the IV estimator when MLR.4 holds (assuming MLR. 1, MLR.2, MLR.3 and MLR.5 also hold)? Explain why or why not. ii. Can the Gauss-Markov Theorem be used to rank the variances of the OLS estimator and the IV estimator when MLR.4 fails? Explain why or why not.2.8 Generate a sequence of 1000 samples of a Gauss-Markov process described by the recursive relation Xn = pXn-1+ W. n = 1, 2. .. . . 1000 where Xo = 0, p = 0.9, and { W, ) is a sequence of zero-mean and unit variance i.i.d. Gaussian random variables.The diagrams below show three Markov chains, where arrows indicate a non-zero transition probability. A Markov Chain 1 State 1 State 2 State 3 B Markov Chain 2 State 1 State 2 State 3 State 4 C Markov Chain 3 State 1 State 2 State whether each of the chains is: e irreducible . periodic, giving the period. [3]