A job in an insurance office involves telephone conversations with policyholders. The office manager estimates that about half of the employee’s time is spent on the telephone. How many observations are needed in a work sampling study to estimate that time percentage to within 6 percent and have a confidence of 98 percent?
377
To determine the number of observations needed in a work sampling study, we can use the following formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = the required number of observations
Z = the Z-score corresponding to the desired confidence level (98% in this case)
p = the estimated proportion of time spent on the telephone (0.5 in this case)
E = the desired error tolerance (6% in this case)
Let's calculate the number of observations using the given values:
Z = 2.33 (corresponding to a 98% confidence level)
p = 0.5
E = 0.06
n = (2.33^2 * 0.5 * (1-0.5)) / 0.06^2
n = (5.4289 * 0.25) / 0.0036
n = 1.35725 / 0.0036
n ≈ 376.4583
Therefore, approximately 376 observations are needed in a work sampling study to estimate the time percentage spent on the telephone with a confidence of 98% and an error tolerance of 6%.
To determine the number of observations needed in a work sampling study, we can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = the number of observations needed
Z = the z-score corresponding to the desired confidence level
p = the estimated proportion (time percentage spent on the telephone)
E = the desired level of precision (margin of error)
In this case:
- The desired confidence level is 98%, which corresponds to a z-score of approximately 2.33.
- The desired level of precision is 6%, which is equivalent to 0.06.
- The estimated proportion, based on the office manager's estimation, is 0.5 (50%).
Now, let's substitute the values into the formula:
n = (2.33^2 * 0.5 * (1-0.5)) / 0.06^2
Simplifying the equation:
n = (5.4289 * 0.25) / 0.0036
n = 1.35725 / 0.0036
n ≈ 376.458
Since the number of observations must be a whole number, we round up to the nearest whole number:
n = 377
Therefore, approximately 377 observations are needed in the work sampling study to estimate the time percentage spent on the telephone with a 98% confidence level and within a 6% margin of error.