Question

A sporting goods manager wants to know what percentage of high school students play tennis. They want their estimate to be accurate within + .02 (E) at the 95% confidence level. If secondary data indicated that 25% of high school students played tennis, how many interviews should be done?

Answer 1

Solution :

Given that,

= 0.25

1 - = 1 - 0.25 = 0.75

margin of error = E =0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= (1.96 / 0.02)2 * 0.25 * 0.75

= 1800.75

Sample size =1801