A survey of food allergies in a random sample of 90 young children found that 6 had some food allergy. (a) Calculate a large sample 95% confidence interval for p, the true population proportion of young children who have a food allergy. (b) Calculate plus four 95% confidence interval for p, the true population proportion of young children who have a food allergy. (c) How large a sample n would you need to estimate p with margin of error 0.04 with 95% confidence? Use the guess p = 0.50 as the value for p. (d) How large a sample n would you need to estimate p with margin of error 0.04 with 95% confidence? Use the sample proportion based on the data collected as the estimated value for p.