Adietician wants to see if there is any difference in the effectiveness of three diets. eighteen people, comprising a sample, were randomly assigned to the three diets. below you are given the total amount of weight lost in a month by each person. diet a diet b diet c14 12 2518 10 3220 22 1812 12 1420 16 1718 12 14what would you advise the dietician about the effectiveness of the three diets? use a .05 level of significance.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.