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A laboratory is testing the concentration level in $\mathrm{mg} / \mathrm{ml}$ for the active ingredient found in a pharmaceutical product. In a random sample of 10 vials of the product, the mean and the sample standard deviation of the concentrations are $2.58 \mathrm{mg} / \mathrm{ml}$ and $0.09 \mathrm{mg} / \mathrm{ml} .$ Find a $95 \%$ confidence interval for the mean concentration level in $\mathrm{mg} / \mathrm{ml}$ for the active ingredient found in this product.
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$n=10, \bar{x}=2.58, \quad S=0.09$

use one - sample $T$, as $\sigma$ unknown

\begin{aligned} \text { DF } = 9 \Rightarrow & t^{*}=2.262 \quad(\mathrm{C}=95 \%) \end{aligned}

$2.58 \pm 2.262 \times 0.09 / \sqrt{10}$

$(2.52,2.64)$
by Diamond (79,336 points)

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