Auto Repairs an Insurance Company Hopes to Save Money on Repairs

question 733

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. $$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Bodies } \\\text { by Bock }\end{array} & \begin{array} { c } \text { Velleman's } \\\text { Automagic }\end{array} \\\hline 2130 & 2570 \\\hline 980 & 1120 \\\hline 3400 & 2950 \\\hline 2190 & 1880 \\\hline 1100 & 1660 \\\hline 1450 & 1700 \\\hline 4590 & 4030 \\\hline 3090 & 3970 \\\hline 1050 & 1130 \\\hline 2530 & 3660 \\\hline\end{array}$$
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.)

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Definitions:

Annuity

A financial product that pays out a fixed stream of payments to an individual, typically used as part of retirement strategy.

Lottery

A form of gambling or a game of chance where participants buy tickets for a chance to win prizes, often financial in nature.

Return

The gain or loss on an investment over a specific period, represented as a percentage of the investment’s cost.

Ordinary Annuity

An annuity where the payment or receipt occurs at the end of each period, such as bonds or leases that make consistent payments.