Question

Answer 23-24 You wish to estimate with 97% confidence, and within 3.5% of true population the proportion of computers that need repairs by the time the product is three years old. 23. No preliminary estimate is available, find the minimum sample size. [961] 24. Find the minimum sample size if a previous study found 19% of computers need repairs within 3 years. [592 computers]

Answer 1

$\mathbf{SOLUTION}$

$\mathbf{given:}\;confidence \;level\;(C)=0.97,\;margin\;of\;error\;(E)=0.035$

$\mathbf{for \;97\%\; confidence\; level,\; Z_{\frac{\alpha }{2}}=2.170}$

C 97 Z* 2.170

$\mathbf{confidence\; level\;calculator\;download\;link:}$

https://drive.google.com/open?id=1miDykB956rSHGgAYD93YaJKxmD9a_oZ1

$\mathbf{formula:}\;sample\;size\;(n)=\left [ \frac{Z_{\frac{\alpha }{2}}}{E} \right ]^{2}*\left [ p*(1-p) \right ]$

$\mathbf{{\color{Blue} 23}.}\;p=0.5\;(no\;preliminary\;estimate)$

$n=\left [ \frac{2.170}{0.035} \right ]^{2}*\left [ 0.5*(1-0.5) \right ]$

$n=\left [ \frac{2.170}{0.035} \right ]^{2}*\left [0.25 \right ]$

$n=\mathbf{{\color{Red} 961}}$

$\mathbf{{\color{Blue} 24}.}\;p=0.19$

$n=\left [ \frac{2.170}{0.035} \right ]^{2}*\left [ 0.19*(1-0.19) \right ]$

$n=\left [ \frac{2.170}{0.035} \right ]^{2}*\left [0.1539 \right ]$

$n=591.5916$

$n\approx \mathbf{{\color{Red} 592}}$