5. Researchers studied three different types of diets and whether or not participants dropped out of a study on losing weight. The data are below in the table: Dropped Out? a. If the researchers chose a random sample of 312 individuals with a desire to lose weight, then let them choose their own diet, and followed them to see h0w many dropped out by the end of the study, what type of sampling was used (Poisson, multinomial, or binomial)? Would this be an observational study or a randomized experiment? Is this study prospective, retrospective, or neither? b. If the researchers chose a random sample of 312 individuals, then randomly assigned 104 to the Low-Fat diet, 99 to the Mediterranean diet, and 109 to the Low-Garb diet, then followed them to see how many dropped out by the end of the study, what type of sampling was used (Poisson, multinomial, or binomial)? Would this be an observational study or a randomized experiment? Is this study prospective, retrospective, or neither? c. Assuming the sampling method described in part (a), calculate the following: o i. Estimated probability of choosing the Low-Fat diet and dropping out of the study. I ii. Estimated probability of dropping out of the study if or given the individual chose the Low-Fat diet. 0 iii. Estimated probability of dropping out of the study. d. If the researchers used the sampling method described in part (b), can you use these data to estimate the probability that an individual with a desire to lose weight will choose the Low-Fat diet? Explain