Final answer:
The statement is true, as about 95% of confidence intervals constructed at the 95% confidence level will contain the population parameter if the procedure were repeated many times. Confidence intervals provide a range likely to include the population parameter, and larger samples usually yield more accurate intervals.
Step-by-step explanation:
The statement, "If we repeated the procedure many times, we would expect about 95% (or whatever statistic) of the intervals to contain the population parameter," is referring to the concept of confidence intervals in statistics. This is a true statement, as confidence intervals are constructed to capture the true population parameter a certain percentage of the time. This percentage is the confidence level. For instance, in the context of a 95% confidence interval, if the process of selecting random samples and creating confidence intervals from these samples was repeated many times, we would expect that roughly 95% of these intervals would indeed contain the actual population mean or proportion.
What this means is that the confidence interval is a range of values, derived from sample data, that is likely to include the true population parameter with a specified level of confidence. For example, if we generated 100 95% confidence intervals for the mean statistics exam score, we would anticipate that about 95 of them would encompass the true population mean exam score. However, please be aware, this does not mean that there's a 95% chance that any given interval includes the population mean, rather that over many samples, 95% of such intervals, on average, will capture the population mean.
Moreover, the accuracy of confidence intervals is influenced by factors such as sample size and variance within the data. Larger samples tend to yield more reliable interval estimates, as smaller sample sizes often result in increased variability. Thus, to have greater confidence that the interval contains the population mean (especially with smaller samples), the interval typically needs to be larger.