Consider the following argument:
'An independent consumer advocacy group sought to determine the reliability of the newly released Zephyr X-series washing machines. They mailed satisfaction questionnaires to 10,000 people who had purchased a Zephyr X-series machine within the last six months. Of the 1,500 people who returned the questionnaire, nearly 90 percent reported experiencing at least one major mechanical failure. Based on this data, the group concluded that the Zephyr X-series is highly unreliable.'
The primary logical flaw in this argument is that it draws a broad conclusion from a sample size (1,500 respondents) that is statistically too small to represent the experiences of all purchasers.
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False
The statement is false because it misidentifies the methodological flaw. The argument's weakness is not the size of the sample, but its unrepresentative nature. People who experience mechanical failures are disproportionately more motivated to return a satisfaction questionnaire than those whose machines function perfectly. This creates a voluntary response bias. A sample of 1,500 is statistically large enough to form a generalization if the sample is randomly selected and representative, so sample size is not the logical flaw here.
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Distinguishing between inadequate sample size and unrepresentative sample bias (voluntary response bias).