A preliminary survey indicates that 20% of the time of workers is spent idly. What is the total number of observations required to determine the proportion of idle time within +/– 5% with 95% confidence limit ? (Take Z values as 2·0)
- A256Correct
- B128
- C512
- D1024
Solution
Concept
Number of observations in work sampling
Formula
N = Z² p (1 − p) / E²
Step-by-step solution
1. p = 0.20, E = 0.05 (absolute), Z = 2. 2. N = 4 × 0.20 × 0.80 / (0.05)² = 0.64 / 0.0025 = 256.
Explanation
Work sampling uses the binomial approximation. The required sample size depends on the proportion, the permitted error and the confidence level.
Why the other options are wrong
128 uses a looser error, while 512 and 1024 correspond to errors of about 3.5% and 2.5%.
Shortcut
N = 4 p (1 − p) / E² for 95% confidence.
Common mistake
Taking the error as 5% of p (relative) which gives 6,400.
Correct answer: A) 256