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Difficulty: MediumStatistical Sampling and Studies

A dermatologist at a medical clinic wants to estimate the proportion of residents in a city who experience seasonal dry skin. The dermatologist surveys a random sample of 150 patients who visited the clinic in December and finds that 90 of them (60%) reported experiencing seasonal dry skin. Which of the following is the most appropriate conclusion based on this study?

  1. A
    Approximately 60% of all residents in the city experience seasonal dry skin.
  2. B
    Approximately 60% of all residents in the city who visit any medical clinic in December experience seasonal dry skin.
  3. No reliable conclusion can be drawn about the proportion of all residents in the city who experience seasonal dry skin because the sample is not representative of the city's population.Answer
  4. D
    Exactly 60% of the residents who visit this specific clinic throughout the entire year experience seasonal dry skin.

Answer

No reliable conclusion can be drawn about the proportion of all residents in the city who experience seasonal dry skin because the sample is not representative of the city's population.
The correct conclusion is that no reliable conclusion can be drawn about all residents of the city. For a sample's findings to be generalized to a larger population, the sample must be randomly selected from that population. In this study, the sample is composed of patients at a dermatology clinic, who are more likely to have skin concerns, and the study was done in December, when dry skin is seasonally more common. Therefore, the sample is not representative of the city's general population, and we cannot generalize the 60% statistic to the entire city.

Step-by-Step Solution

1
Identify the population of interest and the sample group.
The population of interest is all residents of the city. The sample group is 150 patients visiting a dermatology clinic in December.
Understanding the relationship between the sample and the population is necessary to determine if generalization is valid.
2
Evaluate whether the sample is representative of the population of interest.
The sample is not representative because dermatology patients are more likely to have skin issues than the average resident, and December is a winter month when dry skin is more common.
A sample must be randomly selected and representative of the target population to allow for valid generalization.
3
Select the conclusion that reflects the limitation of the sample.
The only appropriate conclusion is that no reliable conclusion can be drawn about the general city population from this biased sample.
Since the sample is biased and non-representative, generalizing the results would lead to an incorrect conclusion about the population of all city residents.

Key Concept

Generalizability of study results based on sample selection and representativeness.
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Topics

Statistical Sampling and Studies

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