Question

Two opposing opinions were shown to a random sample of 1,744 US buyers of a particular political news app. The opinions, shown in a random order to each buyer, were as follows:

Opinion A: Prescription drug regulation is more important than border security.
Opinion B: Border security is more important than prescription drug regulation.

Buyers were to choose the opinion that most closely reflected their own. If they felt neutral on the topics, they were to choose a third option of "Neutral."

The outcomes were as follows:
30% chose Opinion A, 64% chose Opinion B, and 6% chose "Neutral."

Part A: Create and interpret a 95% confidence interval for the proportion of all US buyers who would have chosen Opinion A. (3 points)

Part B: The number of buyers that chose Opinion A and the number of buyers that did not choose Opinion A are both greater than 10. Why must this inference condition be met? (3 points)

Part C: Would a two-sample z-interval for a difference between proportions be an appropriate procedure to find if the difference in proportions between US buyers who would have chosen Opinion B and US buyers who would have chosen Opinion A is statistically significant? Explain why or why not. (4 points)

Answer 1

Part A:

The 95% confidence interval for the proportion of all US buyers who would have chosen Opinion A is between 0.2785 and 0.3215.

We are 95% confident that the true proportion of all US buyers who would have chosen Opinion A is between 0.2785 and 0.3215.

Observed
0.3	p (as decimal)
523/1744	p (as fraction)
523.2	X
1744	n
0.012	std. error
0.2785	confidence interval 95.% lower
0.3215	confidence interval 95.% upper
0.0215	margin of error

Part B:

Because we need at least 10 successes and 10 failures in the sample.

Part C:

Yes, because all the conditions of two-sample z-interval are met.