Final answer:
The confidence interval (CI) indicates the likelihood that a precision interval contains the true population value, with a 90% or 95% CI typically meaning that 90% or 95% of similar intervals would contain the true value.
Step-by-step explanation:
The likelihood that an identified precision interval contains the true (but unknown) population value is the confidence interval (CI). A confidence interval is an interval estimate for an unknown population parameter and reflects the degree of uncertainty or certainty in an estimate. For instance, if we have a 90% confidence interval, it suggests that if we were to take repeated samples and construct confidence intervals from these samples, we would expect approximately 90% of these intervals to contain the true population parameter. For example, in terms of a statistics exam score, if a 95% confidence interval were constructed, we would anticipate that 95% of such confidence intervals would contain the true mean exam score.
The size of the confidence interval and the level of confidence are closely related – a larger interval often implies a higher confidence level since it's more likely to include the true population parameter. The confidence interval also depends on the sample size (smaller samples lead to more variability), the distribution of the data, and the desired confidence level. A higher confidence level corresponds to a larger alpha (α), which is the probability that the confidence interval does not contain the unknown population parameter.