Question

sport illustrated asked a random sample of divison I colleges athletes, "do you believe performance-enhancing drugs are a problem in colleges?" 36% of the sample said "yes." if sports illustrated wishes to estimate the true proportion concerned about drug use in athletes within 2% with 98% confidence, how many people will they have to interview?

Answer 1

Solution :

Given that,

=36%= 0.36

1 - = 1 - 0.36= 0.64

margin of error = E = 2% = 0.02

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = 2.326 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.326 / 0.02)2 * 0.36* 0.64

=3116.3

Sample size = 3116 rounded