Automobile manufacturer Gruman has identified a vehicle quality issue with the bumpers they are using on their mid-size sedan. Customers with these vehicles are suffering substantial damage and repair costs in low-speed impacts to the bumpers. The company has been soliciting proposals for a new collapsible bumper system to upgrade the performance of their sedans to be equal to the industry average of $400 or less in a collision impact of ≤15 miles per hour (mph). Gruman Engineers believe they have found a bumper system that will meet this requirement. To demonstrate it, they crashed six sedans with this bumper into a barrier at 15 mph, submitted them for repairs and recorded the cost of the repairs. The mean and standard deviation of the costs are found to be $458 and $48, respectively. At the α = .05 significance level, does the test data contradict the manufacturer’s claim that the repair cost does not exceed $400? a)What is known? What information AND data does the problem provide? Provide a bullet-pointed list with complete descriptions of what you know about the problem; include written elements as well as numeric information. b)What is unknown? What are you being asked to address? What is the problem that needs an answer? You will not be describing a statistical outcome. c)What are the data you are provided and what are their relevance in this statistical problem? (i.e. sample, mean, population or other parameters. The two below at minimum must be precisely described.)
Automobile manufacturer Gruman has identified a vehicle quality issue with the bumpers they
are using on their mid-size sedan. Customers with these vehicles are suffering substantial
damage and repair costs in low-speed impacts to the bumpers. The company has been soliciting
proposals for a new collapsible bumper system to upgrade the performance of their sedans to be
equal to the industry average of $400 or less in a collision impact of ≤15 miles per hour (mph).
Gruman Engineers believe they have found a bumper system that will meet this requirement. To
demonstrate it, they crashed six sedans with this bumper into a barrier at 15 mph, submitted them
for repairs and recorded the cost of the repairs. The mean and standard deviation of the costs are
found to be $458 and $48, respectively. At the α = .05 significance level, does the test data
contradict the manufacturer’s claim that the repair cost does not exceed $400?
a)What is known? What information AND data does the problem provide? Provide a bullet-pointed list with complete descriptions of what you know about the problem; include written elements as well as numeric information.
b)What is unknown? What are you being asked to address? What is the problem that needs an answer? You will not be describing a statistical outcome.
c)What are the data you are provided and what are their relevance in this statistical problem? (i.e. sample, mean, population or other parameters. The two below at minimum must be precisely described.)
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