(05.04 MC)

A polling agency showed the following two statements to a random sample of 1,500 18-year-olds who are registered to vote in the United States.

Healthcare statement: Improving the healthcare system should be given priority over improving the education system.

Education statement: Improving the education system should be given priority over improving the healthcare system.

The order in which the statements were shown was selected randomly for each person in the sample. After reading the statements, each person was asked to choose the statement that was most consistent with his or her opinion. The results are shown in the table.

Healthcare Statement	Education Statement	No Preference
39%	54%	7%

Part A: Assume the conditions for inference have been met. Construct and interpret a 98% confidence interval for the proportion of all 18-year-old registered voters in the United States who would have chosen the education statement. (5 points)

Part B: One of the conditions for inference that is met is that the number of those who chose the education statement and the number of those who did not choose the education statement are both greater than 10. Explain why it is necessary to satisfy this condition. (5 points) (10 points)