Answer:
The sample size 'n' = 384
Step-by-step explanation:
Step(i):-
Given data the margin of error = 0.05
The margin of error of the estimation of a population proportion is determined by
[tex]M.E = \frac{Z_{\frac{\alpha }{2} }\sqrt{p(1-p} }{\sqrt{n} }[/tex]
Step(ii):-
In data not given sample proportion 'p' but
we know that [tex]\sqrt{p(1-p} \leq \frac{1}{2}[/tex]
[tex]0.05 = \frac{1.96 X \frac{1}{2} }{\sqrt{n} }[/tex]
cross multiplication, we get
0.05 ×√n = 0.98
[tex]\sqrt{n} = \frac{0.98}{0.05} = 19.6[/tex]
squaring on both sides, we get
n = 384.16≅ 384
Final answer:-
The sample size 'n' = 384
