What is the estimated sample size for conducting work sampling at 25% activity time and a 2% absolute error?

To determine the estimated sample size needed for conducting work sampling, one can use the formula that accounts for the activity time proportion, the desired level of confidence, and the acceptable margin of error. In this case, you're looking at a 25% proportion of time spent on a particular activity and a desired absolute error of 2%.

The formula for estimating sample size in work sampling generally is given by:

[ 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 (for example, 1.96 for a 95% confidence level),

• ( p ) is the estimated proportion of the total time for the activity (0.25 in this case),

• ( E ) is the acceptable margin of error (0.02).

By plugging in the values:

1. Estimate ( p = 0.25 ),

2. Calculate ( (1 - p) = 0.75 ),

3. Use ( Z \approx 1.96 ) for a 95% confidence