Answer:
The sample size n= 2500
A survey with 2500 left-handed people guarantees the given margin error is 2%
Step-by-step explanation:
Explanation:-
The margin of error = [tex]\frac{2 S.D}{\sqrt{n} }[/tex]
here for proportions , the standard deviation (σ) = [tex]\sqrt{p(1-p)} \leq \frac{1}{2}[/tex]
[tex]Margin of error = \frac{2 S.D}{\sqrt{n} } \leq \frac{2(\frac{1}{2}) }{\sqrt{n} }[/tex]
[tex]Margin of error = \frac{1}{\sqrt{n} }[/tex]
now The necessary sample size is
[tex]n= \frac{1}{(M.E)^{2} }[/tex]
Given data the survey in order to get a margin of error of 2%
M.E = 0.02
[tex]n= \frac{1}{(0.02)^{2} } = 2500[/tex]
Conclusion:-
The sample size n= 2500
A survey with 2500 left-handed people guarantees the given margin error is 2%
