Question

Consolidated Power, a large electric power utility, has just built a modern nuclear power plant. This plant discharges waste water that is allowed to flow into the Atlantic Ocean. The Environmental Protection Agency (EPA) has ordered that the waste water may not be excessively warm so that thermal pollution of the marine environment near the plant can be avoided. Because of this order, the waste water is allowed to cool in specially constructed ponds and is then released into the ocean. This cooling system works properly if the mean temperature of waste water discharged is 70°F or cooler. Consolidated Power is required to monitor the temperature of the waste water. A sample of 100 temperature readings will be obtained each day, and if the sample results cast a substantial amount of doubt on the hypothesis that the cooling system is working properly (the mean temperature of waste water discharged is 70°F or cooler), then the plant must be shut down and appropriate actions must be taken to correct the problem. (a) Consolidated Power wishes to set up a hypothesis test so that the power plant will be shut down when the null hypothesis is rejected. Set up the null and alternative hypotheses that should be used. Hou (Click to select) 70 versus Hau (Click to select) temperature of waste water. 70 where u = mean (b) In the context of this situation, interpret making a Type I error, interpret making a Type Il error. 70 (shut down) whenu (Click to select) 70 (water is Type I error: decide (Click to select) cool enough, no shutdown needed) 70 (do not shut down) whenu (Click to select) 70 Type Il error: decide u (Click to select) (water is too warm shutdown needed) (c) The EPA periodically conducts spot checks to determine whether the waste water being discharged is too warm. Suppose the EPA has the power to impose very severe penalties (for example, very heavy fines) when the waste water is excessively warm. Other things being equal, should Consolidated Power set the probability of a Type I error equal to a= .01 or a = .05? Set a = 0.05 to make the probability of a (Click to select) error (Click to select)

Drop down options for question a and be are: greater than

less than or equal to

Drop down options for part c are: type 1 or type 2

smaller or larger

Answer 1

a)

Null and Alternative Hypothesis:

H₀: µ = 70

H₁ : µ > 70

b)

Type I error : decide µ > 70 (shut down) when µ = 70(water is cool enough, no shutdown needed)

Type II error : decide µ = 70 (do not shut down) when µ > 70(water is too warm shutdown needed)

c)

Set alpha = 0.05 to make the probability of a Type II error smaller