Which percent confidence interval will be the widest (i.e., the least precise) for a particular data set that includes exactly 500 cases?

Which percent confidence interval will be the widest (i.e., the least precise) for a particular data set that includes exactly 500 cases? Options: (a) 99% (b) 90% (c) 95% (d) None ✅ Correct Option: (a) 99% Explanation (200+ words): The width of a confidence interval depends primarily on the confidence level, sample size, and variability in the data. When the sample size is fixed (here, 500 cases), the only factor affecting width among the given options is the confidence level. A higher confidence level requires a larger critical value, which increases the margin of error and therefore makes the confidence interval wider. A 99% confidence interval is wider than a 95% or 90% confidence interval because it is designed to be more certain that it contains the true population parameter. This increased certainty comes at the cost of precision. In contrast, lower confidence levels such as 90% produce narrower intervals but with less certainty. Thus, for the same dataset and sample size, the 99% confidence interval will always be the widest and the least precise. This concept is fundamental in inferential statistics and is frequently tested in PPSC exams. 10 PPSC-Related Facts: 1. Higher confidence → wider interval 2. 99% CI is least precise 3. Margin of error increases with confidence 4. Sample size fixed here 5. Confidence intervals estimate parameters 6. Precision inversely related to width 7. Common confidence levels: 90%, 95%, 99% 8. Based on normal distribution 9. Uses critical values (z or t) 10. Frequent PPSC MCQ topic