A survey was taken of randomly selected Americans, age 65 and older, which found that 418 of 1002 mon and 548 of 1057 women suffered from some form of arthritis. a) Are the assumptions and conditions necessary for inference satisfied? Explain. b) Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease. c) Interpret your interval in this context. d) Does this suggest that arthritis is more likely to afflict women than men? Explain. ( A. No, the groups were not independent. B Yes, it was a random sample, less than 10% of the population was sampled, the groups were independent, and there were more than 10 successes and fallures in each group. C, No, more than 10% of the population was sampled O D. No, It was not a random sample, b) Let p, be the sample proportion of senior women suffering from some form of arthritis, and let p, be the sample proportion of senior men suffering from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease, P, -P, The confidence interval is (D) (Round to three decimal places as needed,)