A new design for the braking system on a certain type of car hasbeen proposed. For the current system, the true average brakingdistance at 40 mph under specified conditions is known to be 120ft. It is proposed that the new design be implemented only ifsample data strongly indicates a reduction in true average brakingdistance for the new design.
a. Define the parameter of interest.
b. State the relevant hypotheses.
c. Suppose braking distance for the new system is normallydistributed with σ = 11. Let ?̅ denote the sample average brakingdistance for a random sample of 36 observations. Which values of?̅are more contradictory to H0 than 117.2?
d. What is the P-value in this case? What conclusion isappropriate if α = 0.10?
e. What is the probability that the new design is notimplemented when its true average braking distance is actually 115ft and the test from part (b) is used?
