Final answer:
Increasing the confidence interval to a higher probability requires a higher minimum sample size to ensure the interval accurately represents the true population parameter with the desired level of certainty.
Step-by-step explanation:
If the confidence interval is changed to a higher probability, this would cause a higher minimum sample size. This is because a higher confidence level means that we want to be more certain that our true population parameter lies within the interval we calculate. If we increase the confidence level, we widen the interval, which increases the area under the normal distribution curve that corresponds to this level of confidence. To maintain this level of certainty with a higher confidence level, more samples are needed to reduce variability and ensure the interval is accurate, thus resulting in a larger required sample size. If we're aiming to decrease the error bound while keeping the same confidence level, we would need to increase the sample size before conducting the study.