Use the image and the background knowledge below to answer the questions that are also listed below. Background: A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. She randomly assigns 14 rats to a treatment or control group (7 rats in each group). Rats in the treatment group are given the compound daily for a week , while rats in the control group are given a placebo. The null hypothesis is that the rats given the plant compound consume the same number of calories as the rats given the placebo. The design of the study is a independent measures design. The total calories consumed by the rats are normally distributed. Suppose the mean number of weekly calories consumed by the rats given the compound (treatment group) is 790 w/a standard deviation of 68 & the mean number of calories consumed by the control group is 875 w/a standard deviation of 32. Question 1) What are the required assumptions for the independent measures t-test? *you can select multiple options if they are applicable* OptionA) are the calories calories normally distributed (Option B) is there homogeneity of variance? (Option C) are the observations within each group independent? (Option D) are the two groups independent of each other? Question 2) the value of the Hartley F-Max test is? *answer needs to go up to three decimal places!* Question3) using the image, the critical value for the F-max with a=0.01 is ? **note: in the image the critical value for a=.05 are in regular font and the ones for a=.01 are bold**Question 4) given the results of the f-max test, can the research conclude that the data doesn't provide evidence that the homogeneity of variance assumption has been violated? *note: answer yes or no** Question5) can u still use the independent measures t-test if the homogeneity of variance assumption is violated?