To estimate sample size for work sampling with a desired absolute error of 2%, what is the required sample size given a 95% confidence level and an estimated 25% activity time?

To determine the required sample size for work sampling, the formula that can be used is derived from the understanding of confidence intervals in statistics. Specifically, to achieve a desired absolute error (E) at a given confidence level, the formula for sample size can be expressed as:

[ n = \left(\frac{Z^2 \cdot p \cdot (1 - p)}{E^2}\right) ]

Where:

• ( n ) is the required sample size.

• ( Z ) is the z-value corresponding to the desired confidence level (1.96 for a 95% confidence level).

• ( p ) is the estimated proportion of the activity (in this case, 25% or 0.25).

• ( E ) is the desired absolute error (2% or 0.02).

Now, substituting the values into the formula:

1. Using a 95% confidence level, the z-value is approximately 1.96.

2. The estimated proportion ( p ) is 0.25.

3. The desired absolute error ( E ) is 0.02.

By plugging these values into the formula:

[ n = \left(\frac{(1