The Owner of a Service Station Wants to Determine Whether

question 5

Essay

The owner of a service station wants to determine whether the owners of new cars (two years old or less) change their cars' oil more frequently than owners of older cars (more than two years old). From his records, he takes a random sample of 10 new cars and 10 older cars and determines the number of times the oil was changed for each in the last 12 months. The data are shown below. $$\begin{array}{l}\text { Frequency of oil changes in the past } 12 \text { months }\\\begin{array} { | c | c | } \hline \text { New car owners } & \text { Old car owners } \\\hline 6 & 4 \\\hline 3 & 2 \\\hline 3 & 1 \\\hline 3 & 2 \\\hline 4 & 3 \\\hline 3 & 2 \\\hline 6 & 2 \\\hline 5 & 3 \\\hline 5 & 2 \\\hline 4 & 1 \\\hline\end{array}\end{array}$$ Do these data allow the service station owner to infer at the 10% significance level that new car owners change their cars' oil more frequently than older car owners?

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Definitions:

Ciliary Body

A part of the eye that includes the ciliary muscle, which controls the shape of the lens for focusing, and the ciliary epithelium, which produces the aqueous humor.

Optic Nerve

The nerve that transmits visual information from the retina to the brain.

Retina

The light-sensitive layer of tissue at the back of the inner eye that converts light images into nerve signals sent to the brain.

Conjunctiva

The thin, transparent membrane that covers the white part of the eyeball and the inner surfaces of the eyelids.