Answer :
24 weeks of data must be randomly sampled to estimate the mean weekly sales.
The data is ∝=0.10
[tex]\sigma=\$ 1200, E=\$ 400$[/tex]
The margin of error is given by this formula:
[tex]$$M E=z_{\alpha / 2} \frac{\sigma}{\sqrt{n}}$$[/tex]
And on this case we have that ME =400 and we are interested in order to find the value of n, if we solve n from equation.
[tex]$$\begin{aligned}n & =\left(z_\alpha\right)^2 \times\left(\frac{\sigma}{E}\right)^2 . \\& =(1.645)^2 \times\left(\frac{1200}{400}\right)^2 \\& =2.706025 \times \frac{1440000}{160000} \\& =24.354225 \approx 24 \\n & =24 \\\end{aligned}$$[/tex]
There are 24 weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athletic footwear.
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