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Difficulty: MediumStatistical Sampling and Studies

A transportation planner wants to estimate the proportion of commuters in a city who regularly use public transit to travel to work. The city has 60,00060,000 commuters. The planner conducts a survey by randomly selecting 300300 commuters from a database of registered transit pass holders in the city and finds that 240240 of them regularly use public transit to travel to work. Which of the following is the most appropriate conclusion based on the design of the survey?

  1. A
    Approximately 80%80\% of all commuters in the city regularly use public transit to travel to work.
  2. B
    Approximately 48,00048,000 commuters in the city regularly use public transit to travel to work.
  3. No reliable conclusion can be drawn about all commuters in the city because the sample is not representative of all commuters.Answer
  4. D
    The survey results are representative of all commuters in the city because the 300300 participants were selected at random.

Answer

No reliable conclusion can be drawn about all commuters in the city because the sample is not representative of all commuters.
The correct option correctly states that no reliable conclusion can be drawn about all commuters in the city. Because the sample was drawn exclusively from registered transit pass holders, it is highly likely to contain a disproportionately high percentage of public transit users. Thus, the sample is biased and cannot be used to generalize to the entire commuter population.

Step-by-Step Solution

1
Identify the target population and the sample source.
Target population: All 60,00060,000 commuters in the city. Sample source: Registered transit pass holders.
To evaluate the validity of a study, we must check if the sample selection source matches the target population.
2
Assess the representativeness of the sample.
The sample is biased because registered transit pass holders are much more likely to regularly use public transit than a typical commuter in the city.
A representative sample must give every member of the target population an equal chance of selection.
3
Determine the appropriate scope of generalization.
Since the sample is not representative of all commuters, the results cannot be generalized to the entire city population.
Generalization is only valid when the sample is representative of the target population.

Key Concept

Generalizing results from a sample to a population requires a representative, randomly selected sample from that entire population.
Estimated Time:1m 30s
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Topics

Statistical Sampling and Studies

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