After seeing commercials claiming one can get cheaper car insurance online, a local insurance agent was concerned that he might lose 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 accompanying table. Also, his statistical software produced the given summaries. 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 SD(Local - Online) = , SD"(Local) + SD"(Online) . But when he checked, he found that , (229.281) + (256.267) =343.864, not 175.663 as given by the software. Tell him where his mistake is. Eff Click the icon to view the data table i Click the icon to view the software output. Adding These price quotes are for the same cars, so they are Drivers quoted high insurance premiums by the local company will be likely to get a rate from the online company. requires that the variables be X - X Software output Data table Online PriceDiff Variable Count Mean StdDev Local 568 391 177 Local 10 799.200 229.281 872 602 270 Online 10 753. 300 256.267 451 488 - 37 PriceDiff 10 45 .900 175.663 1229 903 326 605 677 - 72 1021 1270 - 249 783 703 80 844 789 55 907 1008 - 101 Print Done 712 702 10 PriceDiff = Local - Online Print Donerate from the online company. Adding requires that the variables be These price quotes are for the same cars, so they are Drivers quoted high insurance premiums by the local company will be likely to get a medians differences means variancesAdding requires that the variables be These price quotes are for the same cars, so they are Drivers quoted high insurance premiums by the local company will be likely to get a rate from the online company. dependent. independent.Adding requires that the variables be These price quotes are for the same cars, so they are Drivers quoted high insurance premiums by the local company will be likely to get a rate from the online company. paired. independent.Adding requires that the variables be These price quotes are for the same cars, so they are Drivers quoted high insurance premiums by the local company will be likely to get a rate from the online company. low moderate high