The paleo diet allows only for foods that humans typically consumed over the last 2.5 million years, excluding those agriculture-type foods that arose during the last 10,000 years or so. researchers randomly divided 500 volunteers into two equal-sized groups. one group spent 6 months on the paleo diet. the other group received a pamphlet about controlling portion sizes. randomized treatment assignment was performed, and at the beginning of the study, the average difference in weights between the two groups was about 0. after the study, the paleo group had lost on average 7 pounds with a standard deviation of 20 pounds while the control group had lost on average 5 pounds with a standard deviation of 12 pounds. (a) the 95% confidence interval for the difference between the two population parameters (paleo - control) is given as (-0.891, 4.891). interpret this interval in the context of the data. (b) based on this confidence interval, do the data provide convincing evidence that the paleo diet is more effective for weight loss than the pamphlet (control)? explain your reasoning. (c) without explicitly performing the hypothesis test, do you think that if the paleo group had lost 8 instead of 7 pounds on average, and everything else was the same, the results would then indicate a significant difference between the treatment and control groups? explain your