Question

In developing patient appointment schedules, a medical center wants to estimate the meantime 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? How large a sample should be taken for a 99% level of confidence? Use a planning value for the population standard deviation of 10 minutes.

95% Confidence (to the nearest whole number):

99% Confidence (to the nearest whole number):

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 2, σ = 10

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 10/2)^2
n = 96.04

Therefore, the sample size needed to satisfy the condition n >= 96.04 and it must be an integer number, we conclude that the minimum required sample size is n = 97
Ans : Sample size, n = 97 or 96

The following information is provided,
Significance Level, α = 0.01, Margin or Error, E = 2, σ = 10

The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (2.58 * 10/2)^2
n = 166.41

Therefore, the sample size needed to satisfy the condition n >= 166.41 and it must be an integer number, we conclude that the minimum required sample size is n = 167
Ans : Sample size, n = 167 or 166