Question

A company wants to determine the proportion of time workers are idle. In a pilot study, the proportion of idle time was found to be 0.16. If the company wants to be 95% confident (z-value = 1.96) that the estimated value is within 0.03 of the true proportion, the number of observations required in the study should be _______

Answer 1

Concept:

 

Concept:

\(A = Z\sqrt{\frac{{P\left( {1 - P} \right)}}{n}}\)

\(A^2=Z^2\left[\frac{P(1-P)}{n}\right]\)

\(n=Z^2\left[\frac{P(1-P)}{A^2}\right]\)

where

Z = Standard normal variate whose value depends upon the confidence level

n = No. of observations

z = 2 (approx) (For 95% confidence level)

P = Percentage occurrence of an activity

A = Limit of accuracy percentage

Calculation:

Given:

Idle time = 0.16

Percentage occurrence of an activity (P) = 1 - idle time = 1 - 0.16 = 0.84

Limit of accuracy (A) = 0.03

Confidence level = 95%, z = 1.96

\(n=Z^2\left[\frac{P(1-P)}{A^2}\right]\)

\(n = \frac{{{{1.96}^2}\times 0.84\left( {1 - 0.84} \right)}}{{{{0.03}^{2\;}}}}=574\)