A job shop manager wants to determine the proportion of time the workers are idle.The shop employs two types of workers.Type 1 includes three workers and Type 2 includes two workers.The manager suspects that the proportion of idle time is about 20 percent for Type 1 workers and 15 percent for Type 2 workers.If the manager wants a 95 percent confidence level and a degree of precision of + 0.05,how many trips will the observers have to take through the group?
A) Fewer than or equal to 80
B) Greater than 80 but fewer than or equal to 90
C) Greater than 90 but fewer than or equal to 100
D) Greater than 100

Question

Quizplus · Accepted Answer

The formula for calculating the minimum sample size is:

n = (Z^2 * p * q) / E^2

where:
- n: sample size
- Z: Z-score, which corresponds to the desired confidence level (1.96 for 95% confidence)
- p: proportion of idle time (0.2 for Type 1 workers and 0.15 for Type 2 workers)
- q: proportion of non-idle time (0.8 for Type 1 workers and 0.85 for Type 2 workers)
- E: degree of precision (0.05)

For Type 1 workers:

n1 = (1.96^2 * 0.2 * 0.8) / 0.05^2 = 153.44

Since we can't have a fractional number of trips, we round up to the nearest integer:

n1 = 154

For Type 2 workers:

n2 = (1.96^2 * 0.15 * 0.85) / 0.05^2 = 105.59

Again, we round up to the nearest integer:

n2 = 106

To get the total sample size, we need to add the samples for each type and multiply by the number of trips:

n = (3+2) * (154+106) = 5 * 260 = 1300

Therefore, the answer is C: Greater than 90 but fewer than or equal to 100.

A Job Shop Manager Wants to Determine the Proportion of Time