Question

A polling agency recently surveyed 1,000 adults who were selected at random from alargecity and asked each of the adults,"Are you satisfied with the quality of air in the city?"Of those surveyed,78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?

I. Of all adults in the city,78 percent are satisfied with the quality of air in the city.
II. If another 1,000 adults selected at random from the city were surveyed,78 percent of them would report they are satisfied with the quality of air in the city.
III. If 1,000adults selected at random from a differentcity were surveyed,78percent of them would report they are satisfied with the quality of air in the city

A. None
B. II Only
C. I and II only
D. I and III only

Answer 1

The correct answer is A. None of the statements must be true because the proportion of satisfaction from a single survey of a sample cannot be assumed to apply universally to all adults in the city, another sample of adults, or adults from a different city.

Step-by-step explanation:

The question pertains to the interpretation of survey results and the extent to which these results can be generalized to the larger population or to different populations.

Based on the results of a survey where 78% of 1,000 randomly selected adults from a large city reported satisfaction with the air quality, we cannot conclude that exactly 78% of all adults in the city feel the same (Statement I), nor can we expect that another random sample of 1,000 adults from the city (Statement II) or from a different city (Statement III) would yield the same percentage.

Variability in samples is expected due to sampling error, and different populations can have different opinions.

The correct answer is A. None of the statements must be true because surveys provide only an estimate for a population proportion based on a sample, and the proportion could differ in another sample or a different population.