Question

Cora wants to determine a 80 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 she have to get a margin of error less than 0.03? [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,

= 0.50

1 - = 1 - 0.50 = 0.50

margin of error = E = 0.03

Z_/2 = 1.282

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

= (1.282/0.03)² *0.50*0.50

=456.53

sample size = n = 457