2. A study was conducted to see if two groups of subjects were equally likely to have a particular disease. For 99 subjects in group A, 23 had the disease, and for 105 subjects in group B, 44 had the disease. You may assume a random sample was taken from each group, and that the groups are independent. (a) Find the the 95% confidence interval for the difference in proportions of subjects with the disease for group A vs. B. (b) Interpret your interval in terms of the problem. (c) Does your interval suggest that group A is more likely to have the disease? (d) What is the largest significant difference in probability of having the disease you expect these two groups to have based on your confidence interval? (e) If we increased our confidence interval to 99%, would our interval widen or narrow?