Answer:
1,294 people
Step-by-step explanation:
-Given the sample proportion is 69% with a 2% margin of error, the sample size can be calculated as below:
[tex]E=z\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
#We substitute and make n the subject of the formula:
[tex]z_{0.03}=1.555\\\\\therefore 0.02=z\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\(\frac{0.02}{z})^2=\frac{\hat p(1-\hat p)}{n}\\\\n=\frac{0.69(1-0.69)}{(0.02/1.555)^2}\\\\n=1293.0389\\\\n\approx 1294[/tex]
Sample size is usually rounded up.
Hence, at least 1,294 people must be surveyed.
