Respuesta :
Answer:
The sample size 'n' = 347
Step-by-step explanation:
Explanation:-
Step(i):-
Given Margin of error = 6% =0.06
The Margin of error is determined by
[tex]M.E=\frac{Z_{\frac{\alpha }{2} }\sqrt{p(1-p)} }{\sqrt{n} }[/tex]
98% of Z-value
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.02}{2} } = Z_{0.01} =2.326[/tex]
Step(ii):-
We know that [tex]\sqrt{p(1-p} \leq \frac{1}{2}[/tex]
[tex]0.06 = \frac{2.236X\frac{1}{2} }{\sqrt{n} }[/tex]
Cross multiplication , we get
[tex]0.06 \sqrt{n} = 2,236 X \frac{1}{2}[/tex]
[tex]0.06 \sqrt{n} = 1.118[/tex]
[tex]\sqrt{n} = \frac{1.118}{0.06} = 18.63[/tex]
Squaring on both sides, we get
n = 347.20≅347
Final answer:-
The sample size 'n' = 347
