Question

The work sampling study, with 100 observations, revealed 25% idle time of a worker. The number of observations required for ±10% accuracy and 95.45% confidence level is ................. (in integer).

Hint:

To calculate the number of observations needed for work sampling, use the formula that incorporates the desired accuracy and confidence level.

Answer 1

Given:
Total observations = 100
Idle time = 25%
Desired accuracy = ±10%
Confidence level = 95.45% (which corresponds to a z-value of 2 for a normal distribution) The formula for determining the number of observations required is:
\[ N = \left( \frac{z^2 \times p \times (1 - p)}{E^2} \right) \] where:
- \(N\) is the required number of observations,
- \(z\) is the z-value for the desired confidence level (2 for 95.45%),
- \(p\) is the proportion of idle time (25% or 0.25),
- \(E\) is the margin of error (10% or 0.10).
Substitute the values:
\[ N = \left( \frac{2^2 \times 0.25 \times (1 - 0.25)}{0.10^2} \right) \] \[ N = \left( \frac{4 \times 0.25 \times 0.75}{0.01} \right) \] \[ N = \left( \frac{0.75}{0.01} \right) = 75 \] Thus, the required number of observations is 71.