Question

Chrome File Edit Vew History Bookmarks People Window Help Wed 6:08 PM Isabelle aE Take ฮ Test-Catin Ghanem hetps:j/www.mathxl.com/Student PlayerTest.aspx?testld-194393938&centerwin-yes Intersession 2019-M119 (CRN: 71336) Caitlin Gharineh 을 | 1/23/19 6:08 PM Test: Final Exam - Chapters 11, 12, 14 Time Remaining: 01:14:25 Submit Te8t This Question: 1 pt 2 0f9 I completel This Test: 9 pts pcssible Question Helo (al he uses a pre«ious ost mate of 24%? (Round up to thnt bcger

Answer 1

$\mathbf{solution}$

$\mathbf{given:}\;margin\;of\;error\;(E)=2\%=0.02$

$\mathbf{\mathbf{for\; 99\%\; confidence\; level, \;z_{\frac{\alpha }{2}}=2.576}}$

$\mathbf{formula:}\;Margin\;of\;error\;(E)=z_{\frac{\alpha }{2}}*\left \{ \sqrt{\frac{p*(1-p)}{n}} \right \}$

${\color{Blue} \mathbf{(a)}}\;given\;p=0.24$

$0.02=2.576*\left \{ \sqrt{\frac{0.24*(1-0.24)}{n}} \right \}$

$\frac{0.02}{2.576}=\sqrt{\frac{0.24*0.76}{n}}$

$\mathbf{square \;on\; both\; sides}$

$\left (\frac{0.02}{2.576} \right )^{2}=\frac{0.24*0.76}{n}$

$n=\frac{0.24*0.76}{\left (\frac{0.02}{2.576} \right )^{2}}$

$n=3025.9$

$n=\mathbf{{\color{Red} 3026}}$

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${\color{Blue} \mathbf{(b)}}\;given\;p=0.50\;(no\;prior\;estimate)$

$0.02=2.576*\left \{ \sqrt{\frac{0.50*(1-0.50)}{n}} \right \}$

$\frac{0.02}{2.576}=\sqrt{\frac{0.50*0.50}{n}}$

$\mathbf{square \;on\; both\; sides}$

$\left (\frac{0.02}{2.576} \right )^{2}=\frac{0.50*0.50}{n}$

$n=\frac{0.50*0.50}{\left (\frac{0.02}{2.576} \right )^{2}}$

$n=4147.4$

$n\approx \mathbf{{\color{Red} 4147}}$