Final answer:
Single institution studies should not be used to determine p0 and p1, as they may not be representative of larger populations. For smaller error bounds at the same confidence level, increasing the sample size or using the plus-four method for confidence intervals can be considered. It's important to choose an appropriate significance level, with 0.05 being standard for balancing Type I error risk and power.
Step-by-step explanation:
Single institution studies should not be used to determine p0 and p1, as these parameters are intended to represent the probabilities or proportions in the overall population or in two separate populations. When single institution studies are used, they often lack the generalizability required to accurately reflect these broader populations. Ecologists and statisticians recommend that findings from such narrow studies be used in conjunction with more comprehensive, ecosystem-wide studies or multi-institutional research to provide the most accurate and representative data.
To achieve a smaller error bound with the same level of confidence, a study could increase the sample size prior to its commencement. A larger sample size reduces the margin of error and thus results in a tighter confidence interval. Moreover, using alternative methods such as the plus-four confidence interval for p method, particularly when the desired confidence level is high and the sample size is moderate, can improve the precision of the confidence interval around the population proportion.When considering hypothesis testing, one must be mindful of the chosen significance level, α. A lower α such as 0.01 would require more stringent evidence to reject the null hypothesis, while an α of 0.05 is commonly used for a balance between Type I error rate and statistical power.