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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
a. The generalization from the sample to the population of affluent Americans will be reasonable if the sample selection was random, large enough, and the survey was conducted at an appropriate time without any temporary influencing factors. b. It's not reasonable to generalize the result to all Americans because people with different financial statuses might have different preferences on the 'time and money' issue.

Step by step solution

01

- Conditions for Valid Generalization

Identify the conditions which may render the generalization from the sample to the population acceptable, considering the nature of survey and target population. In this case, the sample of affluent Americans should be random and sufficiently large, data should be accurately collected (with low non-response rate), and the time of survey should be appropriate (not during a period when perceptions might be altered by temporary factors).
02

- Evaluating Generalization to all Americans

Consider whether the result from affluent Americans can be generalized to all Americans. Critical analysis is necessary as it pertains to the difference in economic situations.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sample Representativeness
When conducting a survey, it's crucial that the sample accurately reflects the entire population you're intending to analyze. Representativeness ensures that the conclusions drawn from the sample are applicable to the broader population. In the context of the survey on affluent Americans prioritizing time over money, for sample representativeness, it should include individuals from various sub-categories within the affluent bracket to avoid over-representation of a particular group.

For instance, it should not only comprise CEOs but also include entrepreneurs, professionals, and artists who have high incomes. It's also advisable to consider other demographic factors such as age, gender, location, and occupation. A stratified random sampling technique can enhance representativeness by dividing the affluent population into these sub-groups and then randomly selecting survey participants from each stratum.

The process of ensuring sample representativeness can include:
  • Using random sampling methods to avoid selection bias.
  • Stratifying the population to ensure all segments are included.
  • Checking the sample size to determine if it's large enough to capture population diversity.
  • Avoiding sampling at times or locations that may lead to homogeneity in responses.
Data Collection Conditions
The validity of survey results is significantly dependent on how the data is collected. There are a few conditions that enhance the quality of data collection and, subsequently, the trustworthiness of the survey's conclusions. The survey of affluent Americans mentioned would need to ensure respondents are actually within the income bracket specified, and that they understand the questions posed to prevent misinterpretation.

Data collection conditions that safeguard the accuracy of survey findings include:
  • Ensuring the survey is easy to comprehend and answer correctly.
  • Minimizing non-response rates by facilitating participation through multiple channels.
  • Conducting the survey in a neutral setting, where participants feel free to respond honestly without external pressures.
  • Keeping the survey period short to reduce the influence of external, transient factors on the responses.
  • Maintaining privacy and confidentiality to ensure honest and untainted responses.

Additionally, the timing of data collection can influence the outcomes. For example, conducting the survey during an economic recession might skew results due to heightened feelings about financial security.
Population Inference
Inference to the population involves extending the results from the sample to the entire population from which the sample was drawn. It is about determining the degree to which the results for affluent Americans who prefer time over money can be projected onto the broader population of all income levels.

This extrapolation process requires a careful examination of the differences between the sampled population and the general population. Since affluent individuals may have different lifestyle priorities compared to the general population, concluding that 57% of all Americans would prefer more time than money might not be accurate.

The reliability of population inference can be evaluated through:
  • Assessing the similarity between the sample demographics and the entire population's demographics.
  • Understanding the socio-economic factors that differentiate the surveyed group from the general population.
  • Evaluating the extent of variance in the responses provided by the sampled population.

For a valid population inference, the survey's findings should only be applied to the population that matches the sample's characteristics, unless there's sound evidence to suggest that the same tendencies apply across different economic strata.

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Most popular questions from this chapter

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