What describes the 95% confidence interval of a 20% absentee rate in a department of 30 people?

• A. 6% to 34%
• B. 8% to 32%
• C. 13% to 27%
• D. 17% to 23%

Answer: (A)

The 95% confidence interval provides a range of values that is likely to contain the true population parameter—in this case, the absentee rate of 20% for a department of 30 people. To calculate the confidence interval, you typically use the sample proportion, the standard error of the proportion, and a z-score that corresponds to the desired confidence level.

For a proportion of 20%, the expected number of absentees in a sample of 30 would be 6 people (20% of 30). The standard error can be determined using the formula for the standard deviation of a proportion. This involves using the formula for the standard deviation of a binomial distribution, adjusting for sample size, and applying the z-score for a 95% confidence level, which is approximately 1.96.

When these calculations are carried out, the result reflects the range around the 20% absentee rate, leading to the conclusion that the confidence interval spans from 6% to 34%. This means that we are 95% confident that the actual absentee rate in the population would fall within this range.

Thus, the correct choice accurately represents this calculated range, demonstrating an understanding of how to interpret confidence intervals in the context of quality management and statistical