Final answer:
The statement that large sample sizes are better but may be cost-prohibitive is true. Larger sample sizes reduce variability and provide more reliable statistics, but at higher costs. Balancing the statistical benefits with cost is essential in research.
Step-by-step explanation:
The statement 'Large sample sizes are always better but sometimes the cost is prohibitive; thus you must always weigh the statistical benefits of collecting more data.' is generally true. Larger sample sizes help to reduce sampling variability, which makes the statistic derived from such samples more reliable. However, there is a trade-off because increasing the sample size can lead to higher costs and logistical complexities. In scenarios where data collection is expensive or practically challenging, such as crash testing cars or studying rare medical conditions, smaller sample sizes may be inevitable. Even with such limitations, it is possible to draw meaningful conclusions, although there might be greater uncertainty associated with the results. In polling, for instance, a sample size of approximately 1,200-1,500 is often considered sufficient for reliability if the survey methodology is sound. Therefore, while large sample sizes are preferred, researchers must always consider the cost implications and the point at which increasing the sample size no longer yields significant benefits in accuracy relative to the additional cost.