A polling agency showed the following two statements to a random sample of 2,150 adults in the United States.

Equal pay statement: The issue of equal pay should be given priority over increasing the minimum wage.

Minimum wage statement: Increasing the minimum wage should be given priority over the issue of equal pay.

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.

Percent of Sample
Equal Pay Statement Minimum Wage Statement No Preference
50% 42% 8%
Part A: Assume the conditions for inference have been met. Construct and interpret a 99% confidence interval for the proportion of all adults in the United States who would have chosen the minimum wage statement. (5 points)

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