Question

6. A chemist has prepared a product designed to kill a particular type of insect. What sample size should be used if he desires to be 94% confident that he is within 0.02 of the true fraction of insects killed? Z= n=

Answer 1

Solution

given : Margin of error E) = 0.02

Confidence level (C) = 0.94

$\small \alpha =1-C=1-0.94=\mathbf{0.06}$

$\small \frac{\alpha}{2} =\frac{0.06}{2}=\mathbf{0.03}$

Refer Standard normal table/Z-table or use excel function "=NORM.S.INV((1-0.03))" to find the Z-value.

=NORM.S.INVI(1-0.03)) NORM.S.INV(probability)

$\small \mathbf{\therefore Z={\color{Red} 1.881}}$

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

When nothing is known about population proportion, Assume p=0.5

$n=\left [ \frac{1.881}{0.02} \right ]^{2}*\left [ 0.5*(1-0.5) \right ]$

$n=\left [94.05\right ]^{2}*\left [ 0.5*0.5 \right ]$

$n=\left [94.05\right ]^{2}*\left [ 0.25 \right ]$

$n=2211.3506$

Round the value to the nearest whole number.

$\mathbf{n={\color{Red} 2212}}$