Six Sigma Black Belt Certified Practice Exam 2025 – The All-in-One Guide to Master Your Certification!

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

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

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8% to 32%

13% to 27%

17% to 23%

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