Question

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 it reasonable to generalize this result to the population of affluent Americans? b. Would it be reasonable to generalize this result to the population of all Americans? Explain why or why not.

Short answer

Conditions that would make it reasonable to generalize this result to the population of affluent Americans include if a random and representative sample of the group was used in the survey, and if the sample size was statistically significant. However, it would not be reasonable to generalize this result to the population of all Americans without survey data from other income groups, as their circumstances, preferences, and characteristics may be significantly different.

Step-by-step solution

Analysis of Data Collection Condition

A condition that would make it reasonable to generalize this result to the population of affluent Americans is if the data were obtained from a random and representative sample of this group. The sample should be large enough to be statistically significant, meaning the sample size should be sufficient to confidently estimate the behavior or opinion of the entire affluent American population.

Assessment of Generalization to All Americans

Generalizing this result to the population of all Americans would not be reasonable. The original survey was conducted only among affluent Americans, those with incomes of $75,000 or more. However, the characteristics, preferences, and circumstances of these individuals may be significantly different from those of all Americans, including those in other income brackets. Therefore, without survey data from these other groups, it would not be appropriate to generalize this result to all Americans.

Summary of Reasoning

In statistical analysis, making valid generalizations requires careful consideration of the population of interest and the conditions under which the data were collected. If the data were collected from representative and random samples of a specific group, such as affluent Americans, it could be reasonable to generalize these results to that specific group. However, generalizing findings to a broader or different population (e.g., all Americans) requires additional data and sound reasoning, to ensure the generalization is appropriate and reliable.