A simple random sample of 1,000 people is taken to estimate the percentage of Democrats in a large population. It turns out that 543 of the people in the sample are Democrats. The sample percentage is (543/1000) x 100% = 54.3%. The SE for the sample percentage of Democrats is 1.6%. (You don't need to check this calculation.) (a) TRUE or FALSE (circle one): (51.1%, 57.5%) is a 95%-confidence interval for the percentage of Democrats in the population. Explain your answer. (b) TRUE or FALSE (circle one): (51.1%, 57.5%) is a 95%-confidence interval for the percentage of Democrats in the sample. Explain your answer. (c) TRUE or FALSE(circle one): There are about two chances in three for the percentage of Democrats in the population to be in the range (52.7%, 55.9%). Explain your answer.