Question

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with $95\%$confidence and a margin of error no greater than $0.03$. How large a random sample do we need?

Short answer

Sample Size is$n=1068$

Step-by-step solution

Given Information

It is given that

Confidence Level $=95\%$

$E=0.03$

Corresponding to$95\%$, using tables$Z_{\frac{\alpha }{2}}=1.96$

Concept Used

Formula to be used:

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

Calculation 

Putting all values. sample size is calculated as:

$=0.50(1-0.50){\left(\frac{1.96}{0.03}\right)}^2$

$=1067.111$

$\approx 1068$

Hence, sample size is$1068$