Runzheimer International, a management consulting firm specializing in transportation reimbursement, released the results of a survey on July 28, 2005. It indicated that it costs more to own a car in Detroit, an amazing $11,844 a year for a mid-sized sedan, than in any other city in the country. The survey revealed that insurance, at $5,162 annually for liability, collision, and comprehensive coverage, is the biggest single reason that maintaining a car in the Motor City is so expensive. A sample size of 100 car owners in Los Angeles was used to determine if the cost of owning a car was more than 10% less than in Detroit. A hypothesis test with a significance level of 0.01 and a standard deviation of $750 is used. Determine the probability that the test will conclude the cost of owning a car in Los Angeles is not more than 10% less than in Detroit when in fact the average cost is $10,361.
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