The senior management of the electric power utility company let there be light (ltbl) has recently built at considerable expense a state of the art nuclear power plant in Gary Indian. The utility has applied or a start up permit from the environmental protection agency (EPA) which has expressed concern over the potential threat to the ecology of lake Michigan posed by the temperature of the waste water from the plant.
In particular, EPA scientists have established that a power plant's cooling system is working properly when the mean temperature of waste water is 58 degrees Fahrenheit or less. EPA staff believes waste water from LTBS's cooling system does not meet the specification that is they believe waste water from the LTBL cooling system is on average greater than 58 degrees Fahrenheit.
Conduct a hypothesis test. What is the p-value and how much evidence is there to conclude that the power plants cooling system is not working properly.