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Difficulty: Very hardSampling and Survey Flaws

An argument states: 'A public health organization sought to determine the average weekly exercise habits of adults in the nation. The organization mailed a comprehensive questionnaire to 50,000 randomly selected households. Of the 4,200 adults who completed and returned the questionnaire, 78% reported exercising for at least 150 minutes per week. Based on these results, the organization concluded that a strong majority of adults in the nation meet the standard recommendation of 150 minutes of weekly exercise.'

Statement: The organization's argument is flawed primarily because a sample of 4,200 respondents is inherently too small to provide a statistically reliable estimate for an entire national adult population.

Answer: Answer

Answer

The statement is False. The argument's flaw is an unrepresentative sample caused by non-response bias, not an inherently insufficient sample size.
The statement is false because it misidentifies the logical flaw. A sample size of 4,200 is highly robust for a national estimate if the sample is truly random and unbiased. The argument actually suffers from a representativeness flaw (specifically, non-response bias), because the subset of people who take the time to fill out and return a health questionnaire are likely to have vastly different exercise habits than the 45,800 who threw it away.

Step-by-Step Solution

1
Analyze the methodology used in the argument to gather data.
The organization sent 50,000 surveys, but only 4,200 were returned. The conclusion about the national population is based entirely on the habits of those 4,200 respondents.
Understanding how the sample was generated is necessary to identify any methodological flaws.
2
Evaluate the specific criticism made in the provided statement.
The statement claims the argument is flawed specifically because the sample size of 4,200 is 'inherently too small' to represent the national population.
To determine if the statement is true or false, we must assess whether a 'small sample size' is the actual logical violation occurring in the stimulus.
3
Assess the statistical validity of the sample size versus its representativeness.
A sample of 4,200 is mathematically large enough to yield a statistically significant estimate for a national population, provided the sample is unbiased. However, the low response rate introduces severe non-response bias, meaning the 4,200 respondents are unlikely to be representative of the whole.
Distinguishing between sample size (quantity) and sample bias (quality) is critical for accurately diagnosing the flaw.
4
Determine the truth value of the statement.
Because the actual flaw is non-response bias (unrepresentative sample) rather than a small sample size, the statement incorrectly diagnoses the logical error.
An incorrect diagnosis of an argument's flaw makes the evaluative statement false.

Key Concept

Distinguishing between an insufficient sample size and an unrepresentative sample (non-response/voluntary response bias).
Estimated Time:1m 30s
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Topics

Sampling and Survey Flaws

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