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? How large a sample should be taken for a 99% level of confidence? Use a planning value for the population standard deviation of 7 minutes. 95% Confidence (to the nearest whole number): 99% Confidence (to the nearest whole number):

Answer 1

Solution:
		Sample size
	95% Confidence	48
	99% Confidence	82
Working Notes:
95% Confidence
	Sample should be taken for a 95% level of confidence (n)= {[(z-value)(sd)]/E}^2
	Z-value at 95% level of confidence =1.96
	s.d is the standard deviation of population = 7 minutes.
	E= desired margin of error = 2 minutes
	(n)= {[(z-value)(sd)]/E}^2
	=((1.96 x 7)/2)^2
	=47.0596
	=48
99% Confidence
	Sample should be taken for a 99% level of confidence (n)= {[(z-value)(sd)]/E}^2
	Z-value at 99% level of confidence =2.5758
	s.d is the standard deviation of population = 7 minutes.
	E= desired margin of error = 2 minutes
	(n)= {[(z-value)(sd)]/E}^2
	=((2.5758 x 7)/2)^2
	=81.27563409
	=82
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