A community organization wanted to estimate the proportion of residents in a town who support the construction of a new public library. The organization surveyed a random sample of 200 residents who were visiting the current public library on a Saturday afternoon. Of those surveyed, 150 supported the construction of a new library. Which of the following is the most appropriate conclusion?
- The results cannot be generalized to all residents of the town because the sample of people surveyed at the current library is likely biased and not representative of the entire town's population.Cevap
- BApproximately 75% of all residents in the town support the construction of a new library.
- CThe results can be generalized to all residents of the town because a random sample of 200 people is large enough to represent the entire population.
- DBecause 150 out of 200 is 50%, approximately 50% of the people who visit the library on a Saturday support the construction of a new library.
Cevap
The results cannot be generalized to all residents of the town because the sample of people surveyed at the current library is likely biased and not representative of the entire town's population.
The correct option is the one stating that the results cannot be generalized to all town residents because library visitors are likely to support library-related initiatives more than the general public, making the sample non-representative.
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Anahtar Kavram
Generalizing results from a sample to a population requires that the sample be representative and randomly selected from that population.