Six Sigma Black Belt Certified Practice Exam

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

1. 6% to 34%

2. 8% to 32%

3. 13% to 27%

4. 17% to 23%

The correct answer is: 6% to 34%

To determine the 95% confidence interval for a 20% absentee rate in a department of 30 people, we typically use the formula for the confidence interval for a proportion, which involves estimating the standard error and applying a z-score for the desired confidence level. In this case, the absentee rate is 20%, or 0.20 as a proportion. To calculate the standard error (SE) of this proportion, the formula is: SE = sqrt[(p(1-p)/n)] Where: - p is the sample proportion (0.20) - n is the sample size (30) Calculating this gives: SE = sqrt[(0.20 * (1 - 0.20)) / 30] = sqrt[(0.20 * 0.80) / 30] = sqrt[0.016] ≈ 0.1265 To find the 95% confidence interval, you would then use the z-score associated with a 95% confidence level, which is approximately 1.96. The confidence interval is calculated as: Confidence Interval = p ± (z * SE) In our case: Confidence Interval = 0.20 ± (1.96