The Medical Rehabilitation Education Foundation reports that the average cost of rehabilitation for stroke victims is 36.7 (in thousand of dollars). To see if the average cost of rehabilitation is different at a particular hospital, a researcher selects a random sample of 63 stroke victims at the hospital and finds that the average cost of their rehabilitation is 38.2. The standard deviation of the population is 5. At \alpha = 0.01, can it be concluded that the average cost of stroke rehabilitation at a particular hospital is different than 36.7. What is the p-value of the test? What is the standard error of the sample mean?

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