Question

In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. how large a sample should be taken if the desired margin of error is two minutes at a 95% level of confidence? use a planning value for the population standard deviation of eight minutes. round your answer to next whole number. how large a sample should be taken for a 99% level of confidence? use a planning value for the population standard deviation of eight minutes. round your answer to next whole number.

Answer 1

To estimate the mean time spent with each patient, the sample size needed can be calculated using the formula for sample size calculation. For a 95% level of confidence with a margin of error of two minutes, a sample size of 61 should be taken. For a 99% level of confidence, a sample size of 106 should be taken.

Step-by-step explanation:

To determine the sample size needed to estimate the mean time that a staff member spends with each patient, we can use the formula for sample size calculation:

Sample Size = (Z^2 * σ^2) / ME^2

where Z is the z-score associated with the desired level of confidence, σ is the population standard deviation, and ME is the desired margin of error.

For a 95% level of confidence with a margin of error of two minutes, the z-score is 1.96. Plugging in the values, we have:

Sample Size = (1.96^2 * 8^2) / 2^2

Sample Size = (3.8416 * 64) / 4

Sample Size ≈ 61

Therefore, a sample size of 61 should be taken for a 95% level of confidence.

For a 99% level of confidence, the z-score is 2.576:

Sample Size = (2.576^2 * 8^2) / 2^2

Sample Size = (6.6406 * 64) / 4

Sample Size ≈ 106

Therefore, a sample size of 106 should be taken for a 99% level of confidence.