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A random sample of 26 offshore oil workers took part in a simulated escape exercise, and their times (sec) to complete the escape are recorded. The sample mean is $370.69$ sec and the sample standard deviation is $24.36$ sec. Construct a $95 \%$ confidence interval on the true average escape time. Interpret your interval.
in Data Science & Statistics by Diamond (81,058 points) | 22 views

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$n=26$
$\bar{x}=370.69$
$S=24.36$
since population standerd devlation $\sigma$ is not known, use $T$-procedure.

$D F=n-1=25$

$t^{*}(95 \%)=2.060$

A $95 \%$ CI for $\mu$ is

$$
\begin{array}{l}\bar{x} \pm t^{*} \cdot 3 / \sqrt{n} \\ 370.69 \pm 2.060 \times 24.36 / \sqrt{26} \\ \text { margin of errer }\end{array}
$$

$$370.69 \pm 2.060 \times \dfrac{24.36}{\sqrt{26}}$$

We are $95 \%$ confident that the true mean  escape time is between $360.9$ sec and $380.5$ sec.
by Diamond (81,058 points)

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