Answer:
We are given:
[tex]\hat{p}=\frac{278}{700}=0.397[/tex]
[tex]z_{\frac{0.02}{2}}=2.33[/tex] is the critical value at 0.02 significance level
[tex]E=0.035[/tex] is the margin of error
Therefore, the required sample size is:
[tex]n=\hat{p}(1-\hat{p}) \left(\frac{z_{\frac{0.02}{2}} }{E} \right )^{2}[/tex]
[tex]=0.397(1-0.397) \left( \frac{2.33}{0.035} \right)^2[/tex]
[tex]=0.239391 \times 4431.755102[/tex]
[tex]=1060.922286 \approx 1061[/tex]
Therefore, the required sample size n = 1061
