The manufacturer of a particular brand of tires claims they average at least 78,000 km before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 12,800 km. A survey of tire owners was conducted to determine if the mileage of the tires is lower than 78,000 km. From the 44 tires sampled, the mean lifespan was 75,000 km. Testing atα= 1%, can we prove that the data is inconsistent with the manufacturers claim?