According to studies by the Pew Research Center and the United Nations (UN), immigrants have a proven economic benefit. Based on reports, between 2005 and 2015, countries in the Middle East have seen the greatest proportion of immigrants in the world compared to its population size. The UN study stated that in 2015, the United Arab Emirates (UAE) had the highest proportion of immigrants at 88% of 10,000 people.

a. Based on the information provided, calculate the 90% confidence interval estimate for the true population proportion, p, of immigrants in the UAE.

b. What is the largest possible sample size needed to estimate the true population proportion, p, of immigrants within a margin of error of 4% with the same level of confidence interval as in part a.

c. Determine the level of confidence if you wanted to maintain the same sample size given by the UN report with only 80% of the people being immigrants within a margin of error of 1%.