A survey was taken of randomly selected Americans, age 65 and older, which found that 415 of 1001 men and 548 of 1060 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) Are the assumptions and conditions necessary for inference satisfied? Explain. O A. No, more than 10% of the population was sampled. O B. No, it was not a random sample. O C. No, the groups were not independent. O D. 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 failures in each group. b) Let p, be the sample proportion of senior women suffering from some form of arthritis, and let p2 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, P1 - P2- The confidence interval is () (Round to three decimal places as needed.) c) There is 95% confidence, based on these samples, that the proportion of American women, age 65 and older, who suffer from arthritis is between % and ]% than the proportion of American men of the same age who suffer from arthritis. (Round to one decimal place as needed.) more d) Does this suggest that arthritis is more likely to afflict women than men? Select the correct answer below and, if necessary, fill in the answer boxes within your choi less O A. Yes, the entire interval lies above 0. O B. Yes, there is 95% confidence, based on these samples, that about % of senior women suffer from arthritis, while only % of senior men suffer from arthritis. (Round to one decimal place as needed.) O C. No, a conclusion cannot be made based on the confidence interval