Question

if we wanted to estimate the proportion of registered voters nationwide who are concerned about climate change, how many people need to be polled so that we are within 2% of the true proportion with 99% confidence?

a) with 0.03 estimate

b) with no prior estimate

Answer 1

Here confidence level = 99%

Here sample size = n

Margin of error = 2% of true proportion = 0.02

so here p = 0.03

critical test statistic for 99% confidence interval = 2.576

Margin of error = critical test statistic * standard error of proportion

0.02 = 2.576 * sqrt [p * (1-p)/n]

0.02 = 2.576 * sqrt [0.02 * 0.98/n]

n/(0.02 * 0.98) = (2.576/0.02)²

n = 0.02 * 0.98 *  (2.576/0.02)²

n = 325.15 or 325

(b) With no prior estimate so here p = 0.50

n = 0.5 * 0.5 * (2.576/0.02)²

n= 4147.36