Question

In a poll of 700 selected people in the USA who are 50 years or older, 20% said they would prefer a complete overhauling of the social security system. Estimate the population proportion of the USA of 1) 50 years or older who would prefer a complete overhauling of the social security system. Use a 95% confidence level. What is the minimum number of people required that would give a sampling error of only 5%?

Answer 1

Let the required population proportion be pi. The 95% confidence interval for the population proportion is
\[0.2-1.96\sqrt{\frac{0.2(1-0.2)}{700}}<\pi<0.2+1.96\sqrt{\frac{0.2(1-0.2)}{700}}\]