Given :
p = 0.68
margin of error, E = 0.1
99% confident interval
alpha, α = 1 - 0.99
= 0.01
[tex]$\frac{\alpha }{2}=\frac{0.01}{2} = 0.005$[/tex]
∴ [tex]$z_{\alpha/2}=z_{0.005}=2.5758$[/tex] (z-critical value)
Sample size = [tex]$z_{\alpha/2} \times \frac{p(1-p)}{E^2}$[/tex]
[tex]$=(2.5758)^2 \times 0.68 \times \frac{(1-0.68)}{0.1^2}$[/tex]
[tex]$= 6.63475 \times 0.68 \times \frac{0.32}{0.01}$[/tex]
= 144.37
= 145 (rounded off)
Therefore, there are 145 businesses does she need to sample to meet this criteria.
