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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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