Finding the best estimate from an average using a confidence limit.

Last year Groton, Georgia had 512 burglaries. The police chief wants to know the average economic loss associated with burglaries in Groton and wants to know it this afternoon. Since there is not time to
analyze all 512 burglaries, the department's research analyst selects 10 burglaries at random, which show the following losses:

$550, $675, $324, $487, $1,246, $874, $595, $835, $910, and $612

What is the best estimate of the average loss on a burglary? Place an 80% confidence limit around this estimate.

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... outliers but because we are asked to also give a confidence interval we choose the sample mean as estimate (xbar=sum of Xi/n=710.8) and we will also compute the bounds of the 80% confidence interval centered on 710.8.
Because the sample size of 10 is small we cannot use a normal confidence interval but we have to use one based on the
t-distribution. The formulas of the confidence interval ...