Statistics 427 Assignment 4 Spring 2021 Be sure to briefly justify all of your answers. This example is based on data from a study published in Journal of Nutrition. There are theories and evidence which suggest that a restricted calorie diet may prolong lifetimes in mammals. To learn more about this possibility, the investigators conducted an experiment to study the effects of a calorie restricted diet on the lifetime of laboratory mice. For this study the normal diet limited to 85 kcal/week is included to serve as the control (reference) diet. The reduced (50 kcal/week) calorie diet was expected to provide evidence that caloric restriction tends to increase mouse lifetimes. A group of 128 female mice was used for this experiment. These 128 mice were randomly divided into two groups. After an initial weaning period, one group of 71 mice was placed on a calorie restricted diet (restricted50 diet) while the other group of 57 mice was placed on the normal calorie diet (normal85 diet). The lifetime in months was measured for each mouse. An experimental unit is a mouse and the unit of measurement is months. As you will recall from exam 1, where this or the related problem with the restricted 40 diet were considered, the lifetime distributions are both skewed left. Let Y , denote the average lifetime of the n = 71 mice placed on the restricted50 diet and let Y2 denote the average lifetime of the n2 = 57 mice placed on the normal85 diet. We will use the randomization distribution of Y1 - Y2 to make inferences about the corresponding population means #1 and #2. Part 1: Some basics. 1. Clearly define two relevant population means, / and /2, with the subscript 1 indicating restricted and the subscript 2 indicating unrestricted. 2. This experiment was conducted to assess the evidence that mice tend to live longer when their caloric intake is restricted. Formalize this research question as a research hypothesis relating #1 to #2. Provide a clear and complete statement of this hypothesis in words in the context of this problem and explain why your hypothesis is appropriate