Answer:
a) the sample size (n) = 156.25≅ 156
Step-by-step explanation:
Step1 :-
Given the two sample sizes are equal so [tex]n_{1} =n_{2} = n[/tex]
Given the standard error (S.E) = 0.04
The standard error of the proportion of the given sample size
[tex]S.E = \sqrt{\frac{pq}{n} }[/tex]
Step 2:-
here we assume that the proportion of boys and girls are equally likely
p= 1/2 and q= 1/2
[tex]S.E = \sqrt{\frac{p(1-p)}{n} } \leq \frac{\frac{1}{2} }{\sqrt{n} }[/tex]
[tex]\sqrt{n} = \frac{\frac{1}{2} }{S.E}[/tex]
squaring on both sides, we get
[tex]n = \frac{1}{(2X0.04)^{2} }[/tex]
on simplification, we get
n= 156.25 ≅ 156
sample size (n) = 156
verification:-
[tex]S.E = \sqrt{\frac{pq}{n} }= \sqrt{\frac{1}{4X156} } =\sqrt{0.0016}[/tex]
Standard error = 0.04
