A random sample of medical files is used to estimate the proportion p of all people who have blood type B. If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 95% sure that the point estimate will be within a distance of 0.04 from p? $\hat { p }$
A)2401
B)25
C)13
D)1201
E)601

Question

Quizplus · Accepted Answer

To determine the sample size needed, use the formula for sample size estimation for proportions: $ n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2} $. Without a preliminary estimate for p, use p = 0.5 for maximum variability. For a 95% confidence level, Z is approximately 1.96. The margin of error E is 0.04. Plugging these values in, $ n = \frac{(1.96)^2 \cdot 0.5 \cdot 0.5}{(0.04)^2} \approx 601 $.

A Random Sample of Medical Files Is Used to Estimate p^\hat { p }p^​

A Random Sample of Medical Files Is Used to Estimate $\hat { p }$