Question

A recent poll of 700 people who work indoors found that 278 smoke. if the researchers want to be 98% confident of their results to within 3.5 percentage points, how large a sample is necessary?

Answer 1

Answer:

We are given:

$\hat{p}=\frac{278}{700}=0.397$

$z_{\frac{0.02}{2}}=2.33$ is the critical value at 0.02 significance level

$E=0.035$ is the margin of error

Therefore, the required sample size is:

$n=\hat{p}(1-\hat{p}) \left(\frac{z_{\frac{0.02}{2}} }{E} \right )^{2}$

      $=0.397(1-0.397) \left( \frac{2.33}{0.035} \right)^2$

      $=0.239391 \times 4431.755102$

      $=1060.922286 \approx 1061$

Therefore, the required sample size n = 1061