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Difficulty: MediumSampling and Survey Flaws

Consider the following argument:

An independent researcher wanted to determine the average daily screen time of teenagers. The researcher recruited 500 teenagers who were attending an annual weekend video gaming convention and tracked their screen time for a month. The results showed an average of 8 hours of screen time per day. The researcher concluded that teenagers, on average, spend 8 hours per day looking at screens.

Evaluate the following statement about the argument as true or false:

The primary logical flaw in the researcher's argument is that the sample size of 500 is too small to draw a reliable statistical conclusion about the general population of teenagers.

Answer: Answer

Answer

False
The statement is false because it misidentifies the logical flaw. The argument's vulnerability lies in its reliance on an unrepresentative sample (selection bias). Teenagers attending a video gaming convention are practically guaranteed to have higher-than-average screen times compared to the general population. Even if the sample size were 50,000, the conclusion would still be flawed. Therefore, the issue is not the sample size (500 is typically mathematically sufficient), but rather the biased nature of the sample source.

Step-by-Step Solution

1
Analyze the scope of the argument's conclusion relative to its premises.
The conclusion generalizes about all teenagers based on data collected from a sample of 500 teenagers attending a gaming convention.
Identifying the gap between the evidence provided and the broad conclusion drawn reveals potential logical flaws.
2
Identify the primary vulnerability in the argument's sampling methodology.
The sample group (gaming convention attendees) is highly likely to have significantly more screen time than the average teenager, making the sample fundamentally unrepresentative.
A representative sample is required to draw valid generalizations about a larger target population.
3
Evaluate the provided statement against the identified flaw.
The statement inaccurately claims the flaw is a small sample size. In reality, 500 is generally a sufficient sample size if randomized; the actual fatal flaw is selection bias.
Distinguishing between sample size (quantity) and sample representativeness (quality) is necessary to accurately determine the statement's truth value.

Key Concept

Distinguishing between sample size and sample representativeness
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Topics

Sampling and Survey Flaws

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