The manufacturer of the X-15 steel-belted radial truch tire claims that the mean mileage the tire can be driven before the tread wears out is 80,000 km. The standard deviation of the mileage is 8,000 km. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 79,000 km. From Crosset's experience, can we conclude, at a level of significance of 0.05, that the mean mileage of the tire is less than 80,000?

Question

The manufacturer of the X-15 steel-belted radial truch tire claims that the mean mileage the tire can be driven before the tread wears out is 80,000 km.  The standard deviation of the mileage is 8,000 km.  The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 79,000 km.  From Crosset's experience, can we conclude, at a level of significance of 0.05, that the mean mileage of the tire is less than 80,000?

PsyDAG · Answer

Z = (mean1 -mean2)/SE (Standard error of the mean)

SE = SD/√(n-1)

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion cut off by the Z score found.