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

Name For the following word problems state if the problem requires using the Central Limit theorem or if does Not require using the Central limit theorem Circle the correct choice: 1. What is the probability of randomly selecting an adult with an IQ score less than 75? A. Requires the Central limit theorem. B. Does not require the central limit theorem. 2. If 30 cell phones are randomly selected what is the probability the cell phones will last an average of more than 23.8 months? A. Requires the Central limit theorem. B. Does not require the central limit theorem. 3. In general Marine platoons are around 50 strong, if a sample of a given platoon is taken from a population of Marines with a mean weight of 200 pounds and with standard deviation o = 10. What is the probability that the sample mean weight will be less than 196 pounds? A. Requires the Central limit theorem. B. Does not require the central limit theorem. 4. The mean age of baseball players is 27 years. Assuming the age of baseball players are normally distributed and that the average size of a baseball team is 25 players, what is the probability a baseball player is older than 30 years if the player is randomly selected. A. Requires the Central limit theorem. B. Does not require the central limit theorem. 5. Suppose that you have a sample of 81 students from a population with mean u = 500 and with standard deviation o = 108. What is the probability that the sample mean will be greater than 483. A. Requires the Central limit theorem. B. Does not require the central limit theorem. Page 1 of 1M4A1 Discussion Forum: Central Limit Theorem Discussion Board Topics: 1. Explain the central limit theorem. 2. Why is the central limit theorem an important concept in statistics? Discussion Board Guidelines: You will need to respond to a peer's posting, and evidence of critical thinking is required.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.A 3-state Markov chain has transition matrix 0.2 0.8 0 P: 0.2 0.5 0.3 0.2 0.6 0.2 If the initial state is X0 = (0, 0, 1) ,find X1 . Enter your answer as a row vector in the form (0.1,0.2,0.3) X1=I