An automobile manufacturer wishes to test that claim that synthetic motor oil can improve gas mileage (in miles per gallon, or mpg). The table below shows the gas mileages, in mpg, of six cars that used synthetic motor oil. The table also shows the gas mileages in mpg of six cars that were using conventional motor oil (the controls).
$\begin{array}{rrrrrrr}
\hline \text { Synthetic: } & 27 & 27 & 26 & 27 & 27 & 29 \
\text { Control: } & 25 & 25 & 25 & 26 & 27 & 25 \
\hline
\end{array}$
Can you conclude that the mean gas mileage for cars using synthetic motor oil is more than the mean for the controls? Use the $\alpha = 0.05$ level of significance.

Question

An automobile manufacturer wishes to test that claim that synthetic motor oil can improve gas mileage (in miles per gallon, or mpg). The table below shows the gas mileages, in mpg, of six cars that used synthetic motor oil. The table also shows the gas mileages in mpg of six cars that were using conventional motor oil (the controls).
 $\begin{array}{rrrrrrr}
\hline \text { Synthetic: } & 27 & 27 & 26 & 27 & 27 & 29 \
\text { Control: } & 25 & 25 & 25 & 26 & 27 & 25 \
\hline
\end{array}$
Can you conclude that the mean gas mileage for cars using synthetic motor oil is more than the mean for the controls? Use the $\alpha = 0.05$ level of significance.

Quizplus · Accepted Answer

The mean gas mileage for cars using synthetic motor oil is higher than for those using conventional oil, and a statistical test (such as a t-test) could be used to determine if this difference is statistically significant at the $\alpha = 0.05$ level. Given the data provided, without performing the actual calculations, the consistent higher values in the synthetic group suggest a potential for a statistically significant difference. However, to definitively conclude, one must perform the statistical test.

An Automobile Manufacturer Wishes to Test That Claim That Synthetic