This problem is based on the well-known Newcomb data set for the speed of light.

Question

This problem is based on the well-known Newcomb data set for the speed of light.9 It contaims the measurements (in nanoseconds) it took the light to bounce inside a network of mirrors. The numbers given are the time recorded minus 24, 800 ns. We will only use the first ten values. 28 26 33 24 34 -44 27 16 40 -2 Some mishaps in the experimental procedure led to the two unusually low values (-44 and-2). Calculate the 95% C.1.'s for the mean in case when a) all the values are used b) the two outliers are removed Which of the intervals will you trust more and why?

Explanation / Answer

The confidence interval for 95% interval will be u+-1.64*std.

When the two values are taken into account, the mean =18.2 and std dev= 24.7thus interval is (-22.31, 58.7)

Else, when two values are removed, then mean=28.5 and std dev=7.25 thus confidence interval is ( 16.6, 40.39).

The second interval is more representative of the data as the other two value were outliers.

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