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Explain the theoretical and practical trade-offs Dr. Chen faces regarding her survey's sample size, and describe how a power analysis can help her resolve this dilemma.
Case context: Dr. Chen is planning a national survey on sleep hygiene among college students. She knows that a sample of participants would provide high statistical confidence and yield statistics very close to the true population value. However, her research grant only has a budget of dollars allocated for participant recruitment, and each completed survey costs dollars in incentives. Dr. Chen is trying to understand the trade-offs of her sampling decisions.
Question: Explain the theoretical and practical trade-offs Dr. Chen faces regarding her survey's sample size, and describe how a power analysis can help her resolve this dilemma.
Sample answer: Dr. Chen faces a trade-off between statistical confidence and budget constraints. A larger sample size of would yield statistics closer to the true population value and provide higher confidence, but it is practically unfeasible because it exceeds her budget. A smaller sample size of fits within her budget of dollars (at dollars per survey) but will result in lower statistical confidence. A power analysis can help her mathematically balance these factors to determine the minimum sample size required to achieve sufficient confidence without exceeding her budget.
Key points:
- Larger samples yield statistics closer to the true population value and provide greater confidence.
- Practical constraints (e.g., budget) limit the possible sample size (here, to participants).
- A power analysis is used to balance desired statistical confidence with budget constraints.
Rubric: The response must explain: 1) why a larger sample size of is theoretically preferred (closer to true population value, greater confidence) but practically unfeasible (exceeds budget), 2) why a smaller sample size of fits the budget constraint but reduces statistical confidence, and 3) how a power analysis helps Dr. Chen identify the optimal balance between these two factors.
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Research Methods in Psychology - 4th American Edition @ KPU
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