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Using the data statements given below, is the final statement True or False?

A dataset of 450 distance observations has a sample mean of 101.825m.

The known distance (determined previously) is 101.819m

The standard deviation of the dataset is 0.012m.

Final statement: The dataset could be considered to be precise and accurate.

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We can use the confidence interval to see if the recoreded distance of 101.819 is within the interval.

$C I=\bar{x} \pm z \frac{s}{\sqrt{n}}$
where

$C I=$ confidence interval
$\bar{x}=$ sample mean
$z=$ confidence level value
$\boldsymbol{s}=$ sample standard deviation
$\boldsymbol{n}$ = sample size

$C I=101.825\pm 1.96 \frac{0.012}{\sqrt{450}}$

$C =101.825 \pm 0.00111$

i.e. We are 95% confident that $\bar{x}$ lies in the interval  $[101.824-101.826]$.

We see that 101.819 is not in this interval and conclude that the dataset cannot be considered to be precise and accurate.
by Diamond (55,129 points)

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