Question

Sports Illustrated planned to ask a random sample of Division I college athletes, "Do you believe performance-enhancing drugs are a problem in college sports?" How many athletes must be interviewed to estimate the proportion concerned about use of drugs within 2% with 85% confidence?

(A) 1300

(B) 17

(C) 1680

(D) 1295

(E) 2401

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.02

At 85% confidence level

= 1 - 85%  

= 1 - 0.85 =0.15

/2 = 0.075

Z/2 = Z_0.075 = 1.439

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.439 / 0.02)² * 0.5 * 0.5

= 1294.20

sample size = n = 1295

correct option is = D