The NIH-funded CALERIE trial (Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy; https://calerie.duke.edu/) is a randomized controlled trial that aimed to determine the effect of a calorie restriction (CR) intervention on markers of longevity, disease risk, and quality of life in healthy adults without obesity.

a) During the CALERIE trial, participants were randomly assigned (i.e., randomized) to receive either (1) a CR intervention where they were prescribed to reduce their energy intake by 25%; or (2) to an ad libitumintake Control group. The purpose of randomization is to ensure that experimental groups are similar at baseline. If the CR and Control groups are equivalent at baseline, we can infer that changes that occur are due to the intervention (i.e., we can infer a causal relationship between the intervention and the outcomes of interest). What statistical tests, if any, can we use to the hypotheses that the CR and Control groups are similar at baseline with respect to their age[AGEBL], baseline weight[BLCLINWT], and energy intake[KCAL]?

b) Conduct the appropriate statistical test(s) in Stata. Interpret the results and be sure to state the null and alternative hypotheses.

c) The CALERIE participants were followed for two years and had study visits at 6, 9, 12, 18, and 24 months. Consider the research hypothesis that the participants receiving the CR intervention had a significant increase in perceived stress over the first six months (likely because they were starving due to a prescribed 25% reduction in energy intake). How can we test this hypothesis? What are two pieces of information that would tell us whether we had a statistically significant result? Please note that this is a hypothetical question and no analysis in Stata is required for the response.