Auto Repairs an Insurance Company Hopes to Save Money on Repairs

Essay

Auto repairs An insurance company hopes to save money on repairs to autos involved in accidents. Two body shops in town seem to do most of the repairs, and the company wonders whether one of them is generally cheaper than the other. From their files of payments made during the past year they select a random sample of ten bills they paid at each repair shop. The data are shown in the table.
$\begin{array}{|c|c|}\hline \text { Bodies } &\text { Velleman's } \\\text { by Bock } &\text { Automagic }\\\hline 2130 & 2570 \\\hline 980 & 1120 \\\hline 3400 & 2950 \\\hline 2190 & 1880 \\\hline 1100 & 1660 \\\hline 1450 & 1700 \\\hline 4590 & 4030 \\\hline 3090 & 3970 \\\hline 1050 & 1130 \\\hline 2530 & 3660 \\\hline\end{array}$

Indicate what inference procedure you would use to see if there is a significant difference in the costs of repairs done at these two body shops, then decide if it is okay to actually perform that inference procedure. (Check the appropriate assumptions and conditions and indicate whether you could or could not proceed. You do not have to do the actual test.)