A supermarket administrator suspects that idle time is about 20 percent for the cashier and 15 percent for the office clerk.If the administrator wants a 95 percent confidence level and a degree of precision of + 0.05 for both cashier and office clerk,how many TOTAL observations are needed?
A) Fewer than or equal to 200
B) Greater than 200 but fewer than or equal to 300
C) Greater than 300 but fewer than or equal to 400
D) Greater than 400

Question

Quizplus · Accepted Answer

The sample size needed for each group is:n = (Z^2 * p * q) / e^2where:Z is the z-score for the desired confidence levelp is the estimated proportion of idle timeq is the complement of p (1 - p)e is the desired degree of precisionFor the cashier:n = (1.96^2 * 0.20 * 0.80) / 0.05^2 = 245.9For the office clerk:n = (1.96^2 * 0.15 * 0.85) / 0.05^2 = 184.9Therefore, the total number of observations needed is 245.9 + 184.9 = 430.8, which is greater than 200 but less than or equal to 300.

A Supermarket Administrator Suspects That Idle Time Is About 20