Econometric class / stats question

Question

A foreign auto manufacturer claims that its sport car

(selling for $60,000) gets, on average at least 30 mi./gal. To

test this claim, the Consumer Protection Agency hires the G&L

Research Lab to evaluate the car's performance. G&L obtain a

random sample of 25 sports cars, which are then tested under the

optimal conditions specified by the manufacturer. After the

test, G&L issue a report stating that the 25 sports cars

obtained, on average, 28.9 mi./gal. with a standard deviation of

3.8 mi./gal. Does this report confirm the manufacturer's claim

at an alpha (significance level) of 0.05?

Answer 1

Thanks for the good question. I enjoyed thinking about this one. The short answer is "no." It would be nice if life worked this way. Imagine running the 100 yard dash 20 times and then discovering that your opponent's best time is actually within your margin of error. Does that mean you're faster? No. In life, we have to demonstrate superiority. It cannot merely be inferred.