Online insurance. After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles (type of car, coverage, driving record, etc.)

for 10 of his clients and checked online price quotes for their policies. The comparisons are shown in the table.

His statistical software produced the following summaries (where PriceDiff = Local - Online):
Variable Count Mean StdDev Local 10 799.200 229.281 Online 10 753.300 256.267 PriceDiff 10 45.900 175.663 At first, the insurance agent wondered whether there was some kind of mistake in this output. He thought the Pythagorean Theorem of Statistics should work for finding the standard deviation of the price differences—in other words, that SD1Local - Online2 = 2SD21Local 2 + SD21Online2.
But when he checked, he found that 21229.28122 + 1256.26722 = 343.864, not 175.663 as given by the software. Tell him where his mistake is.

Transcribed Image Text:

Local Online PriceDiff 568 391 177 872 602 270 451 488 -37 1229 903 326 605 677 -72 1021 1270 -249 783 703 80 844 789 55 907 1008 -101 712 702 10