An automobile manufacturer wishes to test that claim that synthetic motor oil can improv mileage (in miles per gallon, or mpg). The table below shows the gas mileages, in mpg, o that used synthetic motor oil. The table also shows the gas mileages in mpg of six cars tha using conventional motor oil (the controls).
$\begin{array}{ccccccc}
\hline \text { Synthetic: } & 24 & 28 & 27 & 28 & 26 & 26 \
\text { Control: } & 26 & 25 & 25 & 27 & 27 & 27 \
\hline
\end{array}$

Can you conclude that the mean gas mileage for cars using synthetic motor oil is more the the mean for the controls? Use the $\alpha = 0.05$ level of significance. as
A) Yes
B) No

Question

An automobile manufacturer wishes to test that claim that synthetic motor oil can improv mileage (in miles per gallon, or mpg). The table below shows the gas mileages, in mpg, o that used synthetic motor oil. The table also shows the gas mileages in mpg of six cars tha using conventional motor oil (the controls).
$\begin{array}{ccccccc}
\hline \text { Synthetic: } & 24 & 28 & 27 & 28 & 26 & 26 \
\text { Control: } & 26 & 25 & 25 & 27 & 27 & 27 \
\hline
\end{array}$

Can you conclude that the mean gas mileage for cars using synthetic motor oil is more the the mean for the controls? Use the $\alpha = 0.05$ level of significance. as
A) Yes
B) No

Quizplus · Accepted Answer

To determine if the mean gas mileage for cars using synthetic motor oil is significantly higher than the mean for the controls, a hypothesis test can be conducted. The null hypothesis ($H_0$) would state that there is no difference in mean gas mileage between the two groups, while the alternative hypothesis ($H_1$) would suggest that the mean gas mileage for cars using synthetic oil is higher.Calculating the mean for both groups:- Synthetic: $\frac{24 + 28 + 27 + 28 + 26 + 26}{6} = \frac{159}{6} = 26.5$ mpg- Control: $\frac{26 + 25 + 25 + 27 + 27 + 27}{6} = \frac{157}{6} = 26.17$ mpgThe difference in means is $26.5 - 26.17 = 0.33$ mpg, which is relatively small. Without conducting a formal statistical test (e.g., t-test) and calculating the p-value, we cannot definitively conclude that the difference is statistically significant just based on the means. However, given the small difference and without evidence from a statistical test provided in the question, we cannot conclude at the $\alpha = 0.05$ level of significance that the mean gas mileage for cars using synthetic motor oil is more than the mean for the controls. A formal statistical test would be required to make such a conclusion.

An Automobile Manufacturer Wishes to Test That Claim That Synthetic