Confidence Intervals

Question

A health insurance company wants to know the proportion of admitted hospital patients who

have a type 2 diabetes at Orlando Health hospitals. How large of a sample should be taken to

estimate the proportion within 6% at 93% confidence?

Answer 1

sample size = 0.25 * (z (1-alpha/2) / E)^2

alpha = (100 - 93)/100 = 0.07

1 - alpha/2 = 0.965

z alpha/2 = z score corresponding to 0.965 probability = 1.81

E = 0.06 (percentage converted to decimal)

sample size = 0.25 * (1.81/0.06)^2 = 227.5 ~ 228