Final answer:
Option (A), The 'Confidence Level' is the expected proportion of random intervals containing the parameter of interest across many samples. It affects the width of the 'confidence interval', with a higher level leading to a wider interval, and vice versa.
Step-by-step explanation:
The answer to the student's question is Confidence Level. The confidence level is the expected proportion of random intervals that will contain the parameter of interest if a large number of different samples of a particular size are obtained. This term is integral in the concept of inference statistics, particularly when discussing confidence intervals (CIs). A confidence level, often expressed as a percentage (e.g., 90%, 95%), indicates the degree of certainty in the reliability of the interval estimate.
For example, with a 90% confidence level, if we were to take repeated samples and calculate a confidence interval for each sample, we would expect that 90% of these intervals would contain the true population parameter. Confidence intervals are calculated with a formula that includes the sample mean (point estimate), the margin of error (which accounts for sampling variability), and the confidence level which affects the width of the interval.
When the confidence level is higher, the confidence interval is wider, reflecting less precision but greater certainty that the interval contains the parameter. Conversely, a lower confidence level results in a narrower interval, indicating more precision but less certainty.