A weight-loss business is testing 3 different variations of a diet plan to see which one will be the most effective for their clients. Customers were randomly selected and assigned to one of the 3 diet plans; measurements were taken before and after to determine their weight loss over 1 month of following the assigned diet. The data are shown below.

a. State the null and alternative hypotheses to be tested to see if there is a difference in the average weight loss for the 3 diets. (If possible, express the hypotheses symbolically).

b. Indicate the p-value for the hypothesis test to test the hypotheses in part a.

c. Based on your answer in part b, indicate what can be determined about the difference in the average weight loss for the 3 diets. Be sure to justify your conclusions based on the hypothesis test.

d. Calculate the value of Fisher's LSD that would be used for comparing Diet 2 and Diet 3 (use ? = 0.01).

e. Using your answer in part d, explain why it can be concluded that there is a difference in the mean weight loss for Diets 2 and 3.

data : weight loss in kg for 3 diet plans -

Diet 1 3.8 6 0.7 2.9 2.8 2 2 8.5 1.9 3.1 1.5 3 3.6 0.9 -0.6 1.1 4.5 4.1 9 2.4 3.9 3.5 5.1 3.5

Diet 2 0 0 -2.1 2 1.7 4.3 7 0.6 2.7 3.6 3 2 4.2 4.7 3.3 -0.5 4.2 2.4 5.8 3.5 5.3 1.7 5.4 6.1 7.9 -1.4 4.3

Diet 3 7 5.6 3.4 6.8 7.8 5.4 6.8 7.2 7 7.3 0.9 7.6 4.1 6.3 5 2.5 0.9 3.5 0.5 2.8 8.6 4.5 2.8 4.1 5.3 9.2 6.1

Math 3073 HW # 2, spring 2016 Due on Monday 02/22/2016 NAME: 2 1 0 1. Let A= =1 3 5 Find a non-singular matrix P such that PA is a RREF of A 2. Suppose A is a non-singular matrix. Show that if 48 =0, then 8=0\fAQMF_2019s2_assign4_q.pdf (3: 1 Di, # 2 DI) Probability 5. A 3-state Markov Chain has the following state diagram. 0.2 0.2 0.1 0.5 0.3 0.8 2 0.2 3 0.7 Write down the transition matrix P.Consider the general two-state continuous-time Markov chain with transition rates Q = A 0 (a) lJ'il'rite down the backward equations. (b) Show that for any t 3 D, 1110116) + angt} = A. (e) Solve the backward equations. You may use the fact that the solution of the ordinary differential equation .r'(t) = r1226) + Mt) is :r(t) = 12(0):!\" + eat/u e_\"b(s}ds. Consider a three-state continuous-time Markov chain in which the transition rates are given by The states are labelled 1 and 2. on Q: zoo ion 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. (:3) Use the results of Problem 1 to solve the backward equations of this 3-state Markov chain