A car insurance agent was concerned about losing customers to an online competit

Question

A car insurance agent was concerned about losing customers to an online competitor. To investigate, he randomly selected profiles (type of car, coverage, driving record, etc.) for 7 of his clients and checked online price quotes for their policies. The comparisons are shown to the right. His statistical software produced the displayed summaries (where PriceDif-Local-Online). 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, such that PriceDiff 175 69 -38 327 -103 Loca 87 451 122 39 941 48 901 SD(Local -Online)SD (Local)+SD (Online). But when he checked, he found that 841 78 (250.503) (232.537)341.797, not 151.501 as given by the software. Tell him where his mistake is Variable Count Mean Std Dev Loca 7 806.571 250.503 Online 7 746.286 232.537 PriceDiff7 60.286 151.501 Choose the correct answer below. 0 A. Adding variances requires that the variables be independent. These price quotes are for the same cars, so they are paired. O B. The solution was not divided by the sample size. 0 C. Adding variances requires that the variables be dependent. These price quotes are for different cars, so they are not paired D. The operation under the square root needs to be subtraction.

Explanation / Answer

option A) is correct

basically we have to found variance of difference of price not variance (Local - online)

hence first we should subtract the online from local and then calculate variance

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