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 4i] mph under specied conditions is known to be 120 ft. It is proposed that the new design he impiemented only if sample data strongly indicates a reduction in true average braking distance for the new design. (a) Dene the parameter of interest. 0 13 = true proportion of cars whose braking distances reduced 0 = true proportion of cars whose braking distances did not reduce O p = tIue average braking distance for the new design 0 y = true average braking distance for the old design State the relevant hypotheses. O H0: 13 = 120 Ha: p" 120 O H0: :3 = 120 Ha: p t 120 (b) Suppose braking distance for the new system is normally distributed with o' = 13. Let )7 denote the sample average braking distance for a random sample of 36 observations. which values of 3 are more contradictory to Ho than 117.2? 0 E 2 117.2 0 E s 117.2 What is the Pvalue in this case? (Round your answer to four decimal places.) What conclusion is appropriate if a = 0.10? O The new design does have a mean breaking distance less than 120 feet at 40 mph. 0 The new design does not have a mean breaking distance less than 120 feet at 40 mph. (:3) What is the probability that the new:I design is not implemented when its true average braking distance is actually 115 ft and the test from part (b) is used? (Round your answer to four decimal places.)