A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 feet. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking for the new design. A sampe of 36 observations of the new design resulted in a sample mean of 114.8 ft and a standard deviation of 10 ft.
a. Write the appropriate hypothesis.
b. What would the Type I error be and what the consequence be?
c. What would the Type II error be and what the consequence be?
d. Test your hypothesis at alpha=0.005
e. What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft?