Six Sigma Black Belt Certified Practice Exam

What sample size is required to specify a 95% confidence interval of ±3 units when σ = 10?

1. 7

2. 11

3. 32

4. 43

The correct answer is: 43

To determine the sample size required to achieve a 95% confidence interval with a margin of error of ±3 units when the population standard deviation (σ) is 10, you can use the formula for the sample size in estimating a population mean: n = (Z * σ / E)² Where: - n is the sample size, - Z is the z-score corresponding to the desired confidence level, - σ is the population standard deviation, - E is the margin of error. For a 95% confidence level, the z-score is typically 1.96. In this case, the margin of error (E) is 3 units, and the standard deviation (σ) is 10. Substituting the values into the formula: n = (1.96 * 10 / 3)² n = (19.6 / 3)² n = (6.5333)² n = 42.67 Since the sample size must be a whole number, you round up to the nearest whole number, which gives you 43. Therefore, selecting 43 as the sample size ensures that the width of the confidence interval will cover the specified margin of error with the specified confidence