National Motors has equipped the ZX-900 with a new disk brake system. We define p to be the mean stopping distance (from a speed of 35 mph) of all ZX-900s. National Motors would like to claim that the ZX-900 achieves a shorter mean stopping distance than the 60 ft claimed by a competitor.
a. Set up the null and alternative hypotheses needed to support National Motors' claim.
b. A television network will allow National Motors to advertise its claim if the appropriate null hypothesis can be rejected at α = .05. If a random sample of 81 ZX-900 s have a mean stopping distance of  = 57.8 ft, will National Motors be allowed to advertise the claim? Assume that σ = 6.02 ft and justify your answer using both a critical value and a p-value.