Final answer:
A change in confidence level from 95% to 90% would result in a larger sample size and smaller achieved precision. Option A is correct.
Step-by-step explanation:
Adjusting the confidence level from 95% to 90% introduces a dynamic relationship between sample size and achieved precision in statistical sampling. When transitioning to a lower confidence level, such as 90%, a larger sample size becomes necessary to uphold a comparable level of precision. This phenomenon arises from the inherent trade-off between confidence level and margin of error in statistical inference.
A decrease in the confidence level implies a greater acceptance of variability in the data, which, in turn, necessitates a larger sample size to compensate for this heightened uncertainty. The confidence level represents the degree of certainty that the calculated interval contains the true population parameter. As this level decreases, the range within which the parameter is likely to fall widens, demanding a more extensive sample to encapsulate this expanded range effectively.
Consequently, the relationship between sample size, confidence level, and precision becomes intricately interconnected. While a lower confidence level allows for a broader margin of error, maintaining a consistent level of precision demands an increase in the sample size. This delicate balance underscores the strategic considerations inherent in statistical sampling, where researchers must judiciously align confidence levels and sample sizes to derive meaningful and reliable insights from collected data.