Question

HW 25 #7

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 0.02? Assume we have no prior estimate of the proportion and want a conservative choice for the sample size.

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

Answer 1

Solution,

Given that,

= 0.5

1 - = 0.5

margin of error = E =0.02

At 80% confidence level

= 1 - 80%  

= 1 - 0.80 = 0.2

/2 = 0.1

Z/2 = Z0.1  = 1.282

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

= ( 1.282 / 0.02 )2 * 0.5 * 0.5

= 1027

sample size = n = 1027