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 the 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 the next whole number.

a) Sample size for 95% confidence: 24, Sample size for 99% confidence: 35
b) Sample size for 95% confidence: 35, Sample size for 99% confidence: 51
c) Sample size for 95% confidence: 51, Sample size for 99% confidence: 68
d) Sample size for 95% confidence: 68, Sample size for 99% confidence: 81

Answer 1

To estimate the mean time a staff member spends with each patient, we can use the formula n = (Z * σ / E)². For a 95% confidence level with a margin of error of two minutes, the sample size needed is 25. For a 99% confidence level, the sample size needed is 34.

Step-by-step explanation:

In order to determine the sample size needed to estimate the mean time a staff member spends with each patient, we can use the formula:

n = (Z * σ / E)²

Where n is the sample size, Z is the Z-score for the desired confidence level, σ is the population standard deviation, and E is the desired margin of error

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

n = (1.96 * 8 / 2)² = 24.01

Rounding up to the next whole number, the sample size needed is 25.

For a 99% confidence level, the Z-score is approximately 2.58. Plugging in the values, we get:

n = (2.58 * 8 / 2)² = 33.37

Rounding up to the next whole number, the sample size needed is 34.