Question

in developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. use a planning value for the population standard deviation of twelve minutes. (round your answers up to the nearest integer.) how large a sample should be taken if the desired margin of error is three minutes at a 95% level of confidence?

Answer 1

To estimate the mean time that a staff member spends with each patient, use the formula N = (Z * σ / E)^2, where N is the sample size, Z is the Z-value for the desired confidence level, σ is the population standard deviation, and E is the desired margin of error. Applying the formula, a sample size of 241 is needed.

Step-by-step explanation:

To estimate the mean time that a staff member spends with each patient, we need to determine the sample size required to achieve a desired margin of error at a 95% level of confidence. We can use the formula:

N = (Z * σ / E)^2

Where:

N = required sample size

Z = Z-value for the desired level of confidence (in this case, 1.96 for 95% confidence)

σ = population standard deviation (given as 12 minutes)

E = desired margin of error (given as 3 minutes)

Substituting the given values into the formula, we have:

N = (1.96 * 12 / 3)^2

N = 15.52^2

N ≈ 240.8

Rounding up to the nearest integer, the required sample size is 241.