Final answer:
To determine if the difference in average miles per gallon is statistically significant, more information is needed, such as standard deviations and significance level. With provided information, it isn't possible to determine the percent increase that would be statistically significant. Statistical significance is generally assessed through hypothesis testing, comparing the p-value to the alpha level.
Step-by-step explanation:
When assessing whether a difference in means is statistically significant, one usually performs a hypothesis test. In the context of the question, the difference between the average miles per gallon for cars using regular gasoline versus the experimental fuel seems quite large (292 mpg vs. 36.5 mpg). However, to determine statistical significance, more information is needed, including the standard deviations of each group and the specific significance level we are testing against (commonly 0.05 for a 5% significance level).
Statistically significant differences are often represented by a low p-value, usually less than the chosen significance level, indicating that the observed difference is unlikely to have occurred by random chance. With the provided data, we cannot calculate the exact percent increase that would be statistically significant, as we do not have the standard deviations and other metrics required for such a calculation.
However, if we look at the examples provided for reference, like the fuel economy standards by President Barack Obama or the claim that hybrid sedans have a higher mean mpg than nonhybrid ones, we can see that statistical significance is based on hypothesis testing using a sample's mean, standard deviation, and the sample size to determine the p-value and comparing it to the alpha level set for the test.