Question

Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders.

Answer 1

The size will be "431".

Explanation:

On assuming:

P1 = 0.5

P2 = 0.5

Now,

`q1=1-p1`

`=1-0.5`

`=0.5`

and,

`q2=1-p2`

`=1-0.5`

`=0.5`

Margin's error will be,

E = 0.07

For 96% CI critical will be:

Z = 2.054

So,

Sample size =
`(p1q1+p2q2)* ((Z)/(E))^2`

On putting the estimated values, we get

=
`(0.5* 0.5+0.5* 0.5)* ((2.054)/(0.07))^2`

=
`(0.25+0.25)* (29.3)^2`

=
`(0.5)* (858.49)`

= 431