Question

A polling agency showed the following two statements to a random sample of 1,744 adults in the United States.

Drug statement: Prescription drug regulation should be given priority over border security.

Border statement: Border security should be given priority over prescription drug regulation.

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

Drug Statement	Border Statement	No Preference
30%	64%	6%

Part A: Assume the conditions for inference have been met. Construct and interpret a 95% confidence interval for the proportion of all adults in the United States who would have chosen the drug statement. (3 points)

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

Part C: A suggestion is made to use a two-sample z-interval for a difference between proportions to investigate whether the difference in proportions between adults in the United States who would have chosen the border statement and adults in the United States who would have chosen the drug statement is statistically significant. Is the two-sample z-interval for a difference between proportions an appropriate procedure to investigate the difference? Justify your answer.

Answer 1