The six arrangements are repeated below. Arrangement A Arrangement B Arrangement C Treatment Control Treatment Control Treatment Control Man 1 Woman 1 Man 1 Man 2 Man 1 Man 2 Man 2 Woman 2 Woman 1 Woman 2 Woman 2 Woman 1 Arrangement D Arrangement E Arrangement F Treatment Control Treatment Control Treatment Control Woman 1 Man 1 Man 2 Man 1 Man 2 Man Woman 2 Woman 2 Man 2 Woman 2 Woman 1 Woman 1 (b) For the chip method, two chips are marked "treatment" and two chips are marked "control." Each person selects one chip at random without replacement. (i) Complete the table below by calculating the probability of each arrangement occurring if the chip method is used. Arrangement A B C D E F Probability (ii) For the chip method, what is the probability that Man 1 and Man 2 are assigned to the same group? (c) Sixteen participants consisting of 10 students and 6 teachers at an elementary school will be used for an experiment to determine lunch preference for the school population of students and teachers. As the participants enter the school cafeteria for lunch, they will be randomly assigned to receive one of two lunches so that 8 will receive a salad, and 8 will receive a grilled cheese sandwich. The students will enter the cafeteria first, and the teachers will enter next. Which method, the sequential coin flip method or the chip method, should be used to assign the treatments? Justify your choice. 720 yo secured on the atness of your 6. Consider an experian need to enter a treatment group or a control group in such a wa hat eadi go are identified as Man I, Man 2, Woman 1, and Woman 2. The six p Arrangeme Arrangement B Acangenen C Treatment Control Treatment Control Treatment Control Man 1 Wom Man ! Win 2 Man ! Man 2 Man 2 woman 2 Woman 2 Woman I Arrangement D Arrangement E Arrangement F Treatment Control Treatme Control Woman 1 Man 1 Man 2 Man I Woman 2 Man 2 woman woman 2 Two possible methods of assignment are being considered the sey all coin flip method, as described in part (a), and the chip method. as described in part (). For each method, the order of the assignment will be Man I, Man 2, Woman 1, Woman 2 (a) For the sequential coin flip method, a fair coin is flippe one group has two people. An outcome of tails assigns the person to the treatment group, a is assigns the person to the control group. As soon as one group has two people, the rem g people are a tomanically assigned to the other group. (i) Complete the table below by calculating the probability of each arrangement occurring if the sequential coin flip method is used. Arrangement A B C D E F Probability (ii) For the sequential coin flip method, what is the probability that Man 1 and Man 2 are assigned to the same group