Question

Dylan wants to determine a 95 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. How large of a sample must he have to get a margin of error less than 0.02? [To find n, use the value p* = 1/2 for the sample proportion and the values for z* from a z-table or t-table.]

[Round to the smallest integer that works.] n =

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

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 = 1.960

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

= (1.960 / 0.02)2 * 0.5 * 0.5

= 2400.91

= 2401

n = sample size = 2401