Final answer:
With an increase in sample size, the confidence interval becomes narrower due to decreased sampling distribution error bound, resulting in less variability around the population mean. A larger sample size makes the study more expensive. Also, higher confidence levels lead to wider confidence intervals.
Step-by-step explanation:
When the sample size increases in statistical analysis, the sampling distribution error bound decreases. This results in the confidence interval becoming narrower. Essentially, with a larger sample size, there is less variability and a higher likelihood that the sample mean will be close to the population mean. Conversely, a smaller sample size tends to yield a wider confidence interval due to increased variability and greater uncertainty. It's also important to note that an increased sample size typically involves more resources, making the study more expensive.
If the confidence level were to increase, without adjusting the sample size, you would end up with a wider interval, as a higher confidence level requires capturing a larger area under the normal distribution curve. Thus, to maintain the same level of confidence with a smaller error bound, one would need to increase the sample size prior to the study.
For comparison, a 95 percent confidence interval is generally narrower than a 99 percent confidence interval because the higher confidence level corresponds to a larger error bound, given that it encompasses a greater area of the distribution and therefore a wider range of probable values.