Question

Two opposing opinions were shown to a random sample of 2,150 buyers of a particular political news app in the United States. The opinions, shown in a random order to each buyer, were as follows:

Opinion A: The issue of equal pay is more important than increasing the minimum wage.
Opinion B: Increasing the minimum wage is more important than the issue of equal pay.

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:
50% chose Opinion A, 42% chose Opinion B, and 8% chose "Neutral."

The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met? (5 points)

Answer 1

Ans

The conditions we need for inference on one proportion are:

• Random: The data needs to come from a random sample or randomized experiment. This is met as it is already mentioned that we take a random sample of 2150 buyers

Independent: Individual observations need to be independent. This condition is also met

• Normal: The sampling distribution of p^, with, hat, on top needs to be approximately normal — needs at least 10 expected successes and 10 expected failures.

This is why we need the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10 so that we can say the sampling distribution is normal