The Owner of a Service Station Wants to Determine Whether

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?