Answer: 47
Step-by-step explanation:
Given : Margin of error : [tex]E=0.12[/tex]
Significance level : [tex]\alpha: 1-0.90=0.10[/tex]
Critical value : [tex]z_{\alpha/2}=1.645[/tex]
The formula to find the sample size when no prior proportion exists is given by :-
[tex]n=0.25(\dfrac{z_{\alpha/2}}{E})^2[/tex]
i.e. [tex]n=0.25(\dfrac{1.645}{0.12})^2[/tex]
[tex]=46.9796006944\approx47[/tex]
Hence, the minimum required sample size =47
