Final answer:
Increasing the sample size from 10 to 100 while maintaining the same statistics and a 90 percent confidence level results in a narrower confidence interval due to a decrease in the error bound. This occurs because larger samples provide a more precise estimate of the population parameter, reducing uncertainty.
Step-by-step explanation:
When you change the sample size from 10 to 100 while keeping all other statistics the same, the error bound of the confidence interval is affected. Typically, increasing the sample size leads to a decrease in the error bound, making the confidence interval narrower. This is because a larger sample size provides more information about the population, thus reducing the uncertainty (variability) in estimating the population parameter.
If we keep the 90 percent confidence level and increase the sample size to 100, the confidence interval would become narrower when compared with a sample size of 36. Conversely, if we decrease the sample size to 25, the error bound for the mean would increase, resulting in a wider interval due to more variability within a smaller sample size. This implies that larger sample sizes are generally preferred for more accurate estimation, as they yield more precise confidence intervals with smaller error bounds.