A restaurant manager wants to determine the percent of time the servers are working and idle using work sampling. His calculation shows that he needs to take a sample of 100 based on a z value of 2. If he wants to use a z value of 3, how many more samples does he need to take?
A) 225
B) 125
C) 150
D) 50
E) There is not enough information.

Question

Quizplus · Accepted Answer

The number of samples needed for work sampling can be calculated using the formula $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $n$ is the number of samples, $Z$ is the z-value, $p$ is the proportion of time being measured (working or idle), and $E$ is the margin of error. When the z-value increases, the number of samples needed increases because the confidence level is higher, requiring more precision. The relationship between the z-value and the number of samples is quadratic. If 100 samples are needed for a z-value of 2, then for a z-value of 3 (which is 1.5 times larger), the number of samples needed would increase by $1.5^2 = 2.25$ times. Therefore, for a z-value of 3, the samples needed would be $100 \times 2.25 = 225$. Since he already has 100 samples, he needs 125 more samples to reach 225.

A Restaurant Manager Wants to Determine the Percent of Time