Final answer:
The student's question involves understanding confidence intervals in a mathematical context, particularly within the discipline of statistics. Confidence intervals provide a range that likely contains the true population mean, and the level of confidence, such as 90% or 95%, indicates the probability that the calculated interval contains that true mean.
Step-by-step explanation:
The student's question relates to the concept of confidence intervals in statistics, which is a range of values used to estimate the true population mean of a dataset. A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. In the examples provided, different confidence levels (90%, 95%) are mentioned, indicating the degree of certainty (or confidence) that the interval includes the true population mean.
For instance, stating that 95 percent of all confidence intervals constructed in this way contain the true value of the population mean means that if we took many samples and from each calculated a confidence interval, about 95 percent of these intervals would include the actual population mean. The width of the interval increases with the level of confidence because a wider interval is more likely to contain the true mean.