Question

Which sample will result in the proportion of girls being closest to
1
2
?


A study of
10
kids in a scout troop.


A survey of
25
kids in a middle school math class.


A sample of
40
kids on a school bus.


A collection of
100
kids in the ninth grade.

Answer 1

A collection of 100 kids in the ninth grade.

Reason: the variability of a sample proportion is sqrt[p(1−p)/n], which decreases as n increases. For p = 1/2 the standard errors are 0.158 (n=10), 0.100 (n=25), 0.079 (n=40), and 0.050 (n=100), so the n=100 sample will be closest to 1/2.