Question

According to a newspaper 80% of 600 adults polled by telephone say they think going to Mars is a good idea for the world. Find the 98% CI for the proportion of adults who think that going to Mars is a good investment for the world.

Answer 1

p = 0.8

n = 600

$\alpha=1-0.98=0.02$

$z_{\alpha/2}=z_{0.01}=2.33$

Confidence interval $=(p \pm z_{\alpha/2}*\sqrt{\frac{p*(1-p)}{n}})$

                               $=(0.8 \pm 2.33*\sqrt{\frac{0.8*(1-0.8)}{600}})$

                              

= (0.8±0.038)

                               = (0.762 , 0.838)