Online insurance I After seeing countless commercialsclaiming one can get cheaper car insurance from anonline company, a local insurance agent was concernedthat he might lose some customers. To investigate, herandomly selected profiles (type of car, coverage, drivingrecord, etc.) for 10 of his clients and checked online pricequotes for their policies. The comparisons are shown in the table below. His statistical software produced the fol-lowing summaries (where PriceDiff = Local - Online): At first, the insurance agent wondered whether there wassome kind of mistake in this output. He thought thePythagorean Theorem of Statistics should work forfinding the standard deviation of the price differences—in other words, that SD1Local - Online2 =2SD21Local2 + SD2 1Online2. But when he checked,he found that 21229.28122 + 1256.26722 = 343.864,not 175.663 as given by the software. Tell him where hismistake is. Variable Count Mean StdDevLocal 10 799.200 229.281Online 10 753.300 256.267PriceDiff 10 45.9000 175.663Local Online PriceDiff568 391 177872 602 270451 488 -371229 903 326605 677 -721021 1270 -249783 703 80844 789 55907 1008 -101712 702 10

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.