Question
A polling agency recently surveyed 1,000 adults who were selected at random from a large city 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 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
- None
- II only
- I and II only
- I and III only
The correct answer is: None
Solution:- Option A is correct.
Statement I need not be true. The fact that 78% of the 1,000 adults who were surveyed responded that they were satisfied with the air quality in the city does not mean that the exact same percentage of all adults in the city will be satisfied with the air quality in the city.
Statement II need not be true because random samples, even when they are of the same size, are not necessarily identical with regard to percentages of people in them who have a certain opinion.
Statement III need not be true for the same reason that statement II need not
be true: results from different samples can vary. The variation may be even bigger for this sample since it would be selected from a different city. Therefore, none of the statements must be true.
Choices B, C, and D are incorrect because none of the statements must be true.
Therefore, the correct option is A) None.
In mathematics, a survey is a technique for gathering data that involves posing a series of questions to participants to learn more about their attitudes and behaviors. It is the most typical and affordable method of data collection.
For example, Knowledge of consumer purchasing patterns can be used to understand product demand better and increase sales.
Types of Survey Methods
The procedure for gathering data is referred to as the survey method. Different approaches can help you get the extra information or insights you're looking for. Below is a list of some popular techniques.
Online Survey
Paper Survey
Telephonic Survey
Face-to-Face Interview
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