An experiment will be conducted to test the efficacy of a weight loss supplement. Volunteers will be randomly assigned to take either the supplement or a placebo for 90 days, with 12 volunteers in each group. The subjects will not know which treatment they receive. At the end of the experiment, researchers plan to calculate the mean weight loss for each of the two groups and to construct a Welch's two-sample t-confidence interval for the difference of the two treatment means. Choose whether each of the following assumptions are necessary for the confidence interval to be valid. a. The sample sizes must be equal
b. The population standard deviations must be unequal
c. The distribution of weight loss of the two treatments are approximately normally distributed
d. The volunteers in the supplement group are paired with volunteers in the placebo group
e. The expected number of people who lose weight in each group is at least