Question

US-352 Quiz 5 13 14 15 16 17 2 3 4 5 6 78 910 The county clerk wants to estimate the proportion of retired voters who will need special election facilities. The clerk wants to be 95% (Z-1.96) confident that the sample proportion will only differ from the true population proportion by 0.07. Assume p 0.5. How large a sample must be taken to assure these conditions are met? 203 196 186 149 s Previous SkipI Save & N

Answer 1

Solution :

196

Explanation :

^{$\mathrm{n=\frac{Z_{\frac{\alpha }{2}}^{2}*\pi *(1-\pi )}{e^{2}}}$}

$= \frac{\left(1.96\right)^2\left(0.5\right)\left(1-0.5\right)}{\left(0.07\right)^2}$

$= \frac{\left(1.96\right)^2\left(0.5\right)\left(0.5\right)}{\left(0.07\right)^2}$

$= \frac{\left(1.96\right)^2\left(0.25\right)}{\left(0.07\right)^2}$

$= \frac{3.8416*\left(0.25\right)}{\left(0.07\right)^2}$

$= \frac{0.9604}{\left(0.07\right)^2}$

$=\frac{0.9604}{0.0049}$

$=196$