Question

Use the given data to find the minimum sample size required to estimate the population proportion. margin of​ error: 0.0080.008​; confidence​ level: 9999​%; modifyingabove p with caretp and modifyingabove q with caretq unknown

Answer 1

Formula for the Minimum Sample size $n=(\frac{z}{E})^2\hat{p}\hat{q}$

The least biased estimate for p and q is 1/2.

$z_{\frac{\alpha }{2}}=z_{{0.01}{2}}=2.58$

Thus

$n=(\frac{2.58}{0.08})^2*0.5*0.5$

$n=260.015$

$n\approx260$