Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of medical files is used to estimate the proportion p of all people who have blood type B.

(a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.03 from p? (Round your answer up to the nearest whole number.)
__________medical files

(b) Answer part (a) if you use the preliminary estimate that about 13 out of 90 people have blood type B.
__________ medical files

Answer 1

Solution:

Part a)

Given:

c = confidence level = 85%

E = Margin of Error = 0.03

no preliminary estimate for p is given.

thus p = 0.5

Z_c is z critical value for c = 0.85 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.85) / 2 = 1.85 /2 = 0.9250

Thus look in z table for Area = 0.9250 or its closest area and find corresponding z critical value.

Area 0.9251 is closest to 0.9250 , thus corresponding z value is 1.4 and 0.04

Thus Z_c = 1.44

thus

Part b)

n = 90 and x = 13

thus estimate of p is:

thus