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 60°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 60°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 hypothesis H0 and the alternative hypothesis Ha that should be used. H0: μ (Click to select) 60 versus Ha: μ (Click to select) 60. (b) Suppose that Consolidated Power decides to use a level of significance of α = .05 and suppose a random sample of 100 temperature readings is obtained. If the sample mean of the 100 temperature readings is x¯ = 60.931, test H0 versus Ha and determine whether the power plant should be shut down and the cooling system repaired. Perform the hypothesis test by using a critical value and a p-value. Assume σ = 5. (Round your z to 2 decimal places and p-value to 4 decimal places.) z p-value (Click to select) H0. So the plant (Click to select) shut down and the cooling system repaired.

Answer 1

As the null hypothesis says that temperature of the waste water should be less than or equal to 60oF

and alternate hypothesis is that temperature of waste watere would be more than 60oF

So now as we know the formula for Z value:

Z = X-u/(s.d/sqrt(n))

In this case X = 60.931

s.d = 5

mean (u) = 60

n = 100

Z = (60.931-60)/(5/1000.5)

Z = 0.931 / 0.5

Z = 1.862

Probaility would be 0.96857 (from Z table) so p-value is 0.03143 (1-0.96857)

As p-value 0.03143 is less than 0.05 (accepted range) we can say that temperature data shows significan difference than 60oF at upper side.

So we reject the null hypothesis and accept the alternate hypothesis that the temperature system is not working properly and the temperature of the waste water in the pond is higher than 60oF so we need to shut the plant and colling system replaired as temperature shows significantly higher than 60oF