The Owner of a Service Station Wants to Determine Whether

question 18

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:

Massachusetts Bay Colony

An early English settlement established in the 17th century in the Northeastern United States, pivotal in the history and development of America.

British Caribbean

Refers to the region in the Caribbean once colonized and controlled by Britain, characterized by a history of plantation economies, slavery, and later, emancipation and independence movements.

Yamasee War

A conflict from 1715 to 1717 in the southern British colonies, initiated by the Yamasee and several other Native American tribes against European settlers due to trade abuses and land encroachment.

Slave Trade

The historical trade involving the procurement, transportation, and sale of African people as slaves, primarily to the Americas, until its abolition in the 19th century.