Final answer:
The question involves hypothesis testing and sample size determination for population proportions, which are college-level statistics topics. The formula for finding sample size includes using a Z-score, the estimated proportion, and the margin of error.
Step-by-step explanation:
The question pertains to hypothesis testing for proportions in statistics, which is part of college-level mathematics, specifically inferential statistics. To calculate sample size for a proportion, the following formula is often used: n = (Z² * p' * (1 - p')) / E², where Z is the Z-score associated with confidence level, p' is the estimated sample proportion, and E is the margin of error.
For example 8.14, assuming a population proportion (p') of 0.5 and wanting to be 90% confident with a margin of error of 3%, the sample size n can be computed. Since the Z-score for a 90% confidence interval is approximately 1.645, the sample size formula becomes n = (1.645² * 0.5 * 0.5) / 0.03², which needs to be rounded up to the next higher value to determine the minimum sample size needed.