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 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%?

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 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

Try this formula:

n = [(z-value)^2 * p * q]/E^2
= [(1.96)^2 * .2 * .8]/.05^2

I'll let you finish the calculation.

Note: n = sample size needed; .2 (20%)for p and .8 (which is 1 - p) for q. E = maximum error, which is .05 (5%) in the problem. Z-value is found using a z-table (for 95%, the value is 1.96). Symbols: * means to multiply and ^2 means squared.

I hope this will help get you started.