Answer Happy

Problem 6 A company is currently using a type of high-pressure oil-filled submarine power cable whose standard deviation of sheath thickness is 0.05 mm. Sup- pose a new type of cable is available in the market. Before agreeing to purchase a large order of the new type, the company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than 05 mm. • Specify the null and the alternative hypothesis. • What are the type I and type II errors? Problem 7 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 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design. (a) Define the parameter of interest and state the relevant hypotheses. (b) Suppose braking distance for the new system is normally distributed 10. Let X denote the sample average braking distance for a random sample of 36 observations. Which of the following three rejec- tion regions is appropriate? Ri = {: > 124.80), R2 = {2:ī <115.20}, R3 = {.c:> 125.13 or i < 114.87}. with o = = (c) What is the Type I error rate if R2 is adopted? Refer to the z-table. How would you change the region to obtain a test with a = -0.001? (d) What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft and the appropriate region from part (b) is used?