Question

A major energy producer fi rma built a new nuclear power plant. This power plant discharges waste water, which is allowed to be poured into the Atlantic Ocean. It is known that the discharged water temperature values ​​are normally distributed. The Environmental Protection Agency stated that the temperature of the waste water should not be too high in order to prevent the thermal pollution of the marina near the power plant. If the temperature of the discharged water is 60 degrees or less, it is understood that the cooling system is working properly. To test this, the average of 36 randomly selected temperature values ​​was 60.5 and the standard deviation was 2.

a) Can it be said that the average water temperature at 3% significance level is more than 60 degrees?

b) If the actual temperature is understood 61 degrees, obtain the probability of Type II error and the power of the test.

Answer 1