Answer: 271
Step-by-step explanation:
The formula we use to find the sample size is given by :-
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]
, where [tex]z_{\alpha/2}[/tex] is the two-tailed z-value for significance level of [tex](\alpha)[/tex]
p = prior estimation of the proportion
E = Margin of error.
If prior estimation of the proportion is unknown, then we take p= 0.5 , the formula becomes
[tex]n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2[/tex]
[tex]n=0.25(\dfrac{z_{\alpha/2}}{E})^2[/tex]
Given : Margin of error : E= 0.05
Confidence level = 90%
Significance level [tex]\alpha=1-0.90=0.10[/tex]
Using z-value table , Two-tailed z-value for significance level of [tex]0.10[/tex]
[tex]z_{\alpha/2}=1.645[/tex]
Then, the required sample size would be :
[tex]n=0.25(\dfrac{1.645}{0.05})^2[/tex]
Simplify,
[tex]n=270.6025\approx271[/tex]
Hence, the required minimum sample size =271
