A work sampling method is used to determine the proportion of the time a worker is idle.The following information was gathered on a random basis. If the manager wants a 95 percent confidence level (z = 1.96)and a degree of precision of + 0.03,how many more observations are needed?
A)fewer than or equal to 600
B)greater than 600 but fewer than or equal to 800
C)greater than 800 but fewer than or equal to 1,000
D)greater than 1,000

Question

A work sampling method is used to determine the proportion of the time a worker is idle.The following information was gathered on a random basis.  If the manager wants a 95 percent confidence level (z = 1.96)and a degree of precision of + 0.03,how many more observations are needed?
A)fewer than or equal to 600 
B)greater than 600 but fewer than or equal to 800 
C)greater than 800 but fewer than or equal to 1,000 
D)greater than 1,000

Quizplus · Accepted Answer

To calculate the number of additional observations needed, we use the formula:

n = (z^2 * p * (1-p)) / (d^2)

where:
- z = 1.96 for a 95% confidence level
- p = proportion of time worker is idle (unknown)
- d = degree of precision = 0.03

We don't know the value of p, so we need to estimate it from the data we already have. From the table, we see that out of 100 observations, the worker was idle for 20 of them. So the estimated proportion of idle time is p̂ = 0.20.

Now we can plug in the values:

n = (1.96^2 * 0.20 * 0.80) / (0.03^2) = 846.74

This means we need at least 847 observations in total. We already have 100, so we need to collect 747 more. The closest choice is C, which is between 800 and 1000.

A Work Sampling Method Is Used to Determine the Proportion