You are an associate assigned to the claims department of a major insurance company. A policy holder has had an accident with his classic 1968 Oldsmobile Cutlass Supreme.
At issue is the consideration of his brakes. Recently, he was driving down the road and was apparently unable to stop in time when a woman driving a 2004 Porsche Boxster "S" pulled out in front of him; subsequently, he "T-boned" the Porsche. Injured in the accident were the, driver of the Porsche, who was 7 months pregnant with twins and her elderly mother-in-law who has cerebral palsy; both of which were from out of town. Now with their only means of transportation "totaled" they are stranded.
The Porsche driver's insurance company, which is USA, contends that your policy holder is at fault because his car was not up to current standards. There seems to be a difference in the braking distance between vintage brake shoes and current ones.
Your policy holder is a self proclaimed, "shade tree" mechanic and a classic car enthusiast. As a matter of fact, he once owned a rather successful auto mechanic business and is now the President of the State of Florida Oldsmobile Club which has a substantial lobby in Tallahassee.
Your boss decided that because you are enrolled in a statistics class you should be pressed into service to assist and, as such, you have questioned the policy holder extensively. From your investigation you discover that he does his own work and recently replaced his brakes with a vintage brand of asbestos brake shoes. The contention is that modern brake shoes stop a vehicle which is traveling at 35 mph (which your policy holder was pr oven to be doing) at 20.5 feet, give or take one foot either side.
Your company's research department gathered the following in support:
Out of 42 sets available, worldwide, of vintage asbestos brake shoes, 20 were selected for testing. Below are the results:
23.2 18.1 19.2 20.3 23.0
26.0 24.6 16.9 17.3 23.4
28.6 17.2 23.2 18.7 19.6
20.8 24.2 25.0 19.8 17.6
A. What is the percentage of these pads that fall within the current and
more modem parameters?
B. Arrange this data in class intervals and construct a Frequency
C. Construct a confidence interval to predict the boundaries of this
D. Your policy holder actually contends that the vintage brake shoes exceed the modem standards. Is there evidence that would suggest he is correct?
E. Assuming that the stopping distance between the vintage brake shoe and the modem equivalent is the same, what is the probability that either one tested will stop a vehicle of this size or larger, within 5 feet of the true mean?
F. What is the probability that the difference between the stopping. distance with the vintage brake pads and the stopping distance of the newer style brake pads being as large as reported or larger if there is no difference in the true stopping distance averages between the two styles?
The solution provides step by step method for the calculation of confidence interval and frequency distribution . Formula for the calculation and Interpretations of the results are also included.