Question:

The following data set is derived from two different analytical methods analyzing the same samples. The samples contain different concentrations of acetylsalicylic acid (ASA) added to blood. The two analytical methods are chromatographic methods and only differ in the oven temperature (35 C vs. 45 C) while all other parameters are held constant. Each sample is analyzed 3 times.

Spiked ASA concentration

(in mg/L) Method 1 (35C) )Method 2(45 C)

0.25 20 18 21 25 23 28

0.5 33 31 32 41 38 39

1.0 44 48 45 91 87 95

2.0 71 75 73 136 145 139

4.0 125 119 131 181 172 175

A........Plot the two linear regression models on one set of axes. Then calculate coefficients of determination for each of the two methods (note: you can use any program that is able to calculate simple linear regression models. If you do, please provide the data file in addition to the answer). Which of the methods would you prefer for the analysis of ASA samples over a concentration range of 0.25 to 4 mg/L?

B. Calculate the 95% confidence intervals for the slopes of each of the two regression models. Do these confidence intervals overlap? What conclusions can you draw from the confidence intervals?

C. Test the hypothesis that the two slopes are not significantly different from each other. In order to do so, consider that the each of the slopes is a variable that has a mean and a standard deviation -

PLEASE SHOW ALL STEPS AND EXPLANATION FOR EACH PART>thanks

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 pointsProbability 5. A 3-state Markov Chain has the following state diagram. 0.2 0.2 0.1 0.5 0.3 0.8 N 0.7 0.2 Write down the transition matrix P.Consider a three-state continuous-time Markov chain in which the transition rates are given by Q = 0 0 A O O The states are labelled 1, 2 and 3. (a) Write down the transition matrix of the corresponding embedded Markov chain as well as the transition rates out of each of the three states. (b) Use the symmetry of Q to argue that this setting can be reduced to one with only 2 states. (c) Use the results of Problem 1 to solve the backward equations of this 3-state Markov chain. (d) Obtain the steady-state probabilities of this 3-state Markov chain in two different ways