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A survey of affluent Americans (those with incomes of \(\$ 75,000\) or more) indicated that \(57 \%\) would rather have more time than more money (USA Today, January 29,2003 ). a. What condition on how the data were collected would make the generalization from the sample to the population of affluent Americans reasonable? b. Would it be reasonable to generalize from the sample to say that \(57 \%\) of all Americans would rather have more time than more money? Explain.

Short Answer

Expert verified
When generalizing from a sample to the population, it's crucial to ensure representative sampling. In this case, the sample representation might be valid for affluent Americans if they all had an equal chance of being surveyed. However, generalizing the findings to all Americans regardless of income would be less reasonable, given the different lifestyle and income inequalities among different demographics within the country.

Step by step solution

01

Assessing generalization to the Affluent American population

To correctly generalize from the sample to the entire population of affluent Americans, the survey should have been administered in a way that ensures it is representative of this group. This signifies that every affluent American should have had an equal chance to be part of the survey. This can be achieved through random sampling methods.
02

Analyzing generalization to the Entire American population

Expand the reasoning from step 1 to consider the population of all Americans, including those not classified as affluent. The survey result of \(57 \%\) of affluent Americans preferring more time than money might not be applicable to all Americans. This is mainly because the income level and lifestyle of affluent Americans may differ significantly from others, thereby influencing their preference.

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