Which of the following is not true of the confidence level of a confidence interval?

• A. A higher $\mathrm{confidence} \mathrm{level}$ results in a wider $\mathrm{confidence} \mathrm{interval}$, all else being equal.
• B. The $\mathrm{confidence} \mathrm{level}$ represents the proportion of similarly constructed intervals that would contain the $\mathrm{population} \mathrm{parameter}$ in repeated sampling.
• C. Common $\mathrm{confidence} \mathrm{levels}$ include $90\%$, $95\%$, and $99\%$.
• D. The $\mathrm{confidence} \mathrm{level}$ indicates the probability that the specific calculated interval contains the $\mathrm{population} \mathrm{parameter}$.

Answer: (D)

Verified step by step guidance

1. Understand the definition of a confidence level: It represents the proportion of confidence intervals, constructed in the same way from repeated samples, that would contain the true population parameter.
2. Recognize that a higher confidence level means we want to be more certain that the interval contains the parameter, which leads to a wider confidence interval to account for more variability.
3. Recall common confidence levels used in practice, such as 90%, 95%, and 99%, which reflect different degrees of certainty.
4. Note that the confidence level does NOT represent the probability that a specific calculated interval contains the population parameter; once the interval is calculated, the parameter either is or is not in that interval.
5. Therefore, the statement 'The confidence level indicates the probability that the specific calculated interval contains the population parameter' is incorrect because the confidence level refers to the long-run proportion of intervals that contain the parameter, not the probability for a single interval.